{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:18:06Z","timestamp":1776784686150,"version":"3.51.2"},"reference-count":8,"publisher":"American Mathematical Society (AMS)","issue":"252","license":[{"start":{"date-parts":[[2006,3,15]],"date-time":"2006-03-15T00:00:00Z","timestamp":1142380800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We know from Littlewood (1968) that the moments of order\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"4\">\n                        <mml:semantics>\n                          <mml:mn>4<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of the classical Rudin\u2013Shapiro polynomials\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper P Subscript n Baseline left-parenthesis z right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>P<\/mml:mi>\n                              <mml:mi>n<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>z<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">P_n(z)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    satisfy a linear recurrence of degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2\">\n                        <mml:semantics>\n                          <mml:mn>2<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . In a previous article, we developed a new approach, which enables us to compute exactly all the moments\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper M Subscript q Baseline left-parenthesis upper P Subscript n Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:msub>\n                                <mml:mi>P<\/mml:mi>\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:msub>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathcal {M}_q({P_n})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of even order\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q\">\n                        <mml:semantics>\n                          <mml:mi>q<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">q<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q less-than-or-slanted-equals 32\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo>\n                              \u2a7d\n                              \n                            <\/mml:mo>\n                            <mml:mn>32<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">q\\leqslant 32<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We were also able to check a conjecture on the asymptotic behavior of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper M Subscript q Baseline left-parenthesis upper P Subscript n Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:msub>\n                                <mml:mi>P<\/mml:mi>\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:msub>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathcal {M}_q({P_n})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , namely\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper M Subscript q Baseline left-parenthesis upper P Subscript n Baseline right-parenthesis tilde upper C Subscript q Baseline 2 Superscript n q slash 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:msub>\n                                <mml:mi>P<\/mml:mi>\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:msub>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>\n                              \u223c\n                              \n                            <\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>C<\/mml:mi>\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:msup>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>n<\/mml:mi>\n                                <mml:mi>q<\/mml:mi>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathcal {M}_q({P_n})\\sim C_q 2^{nq\/2}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , where\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C Subscript q Baseline equals 2 Superscript q slash 2 Baseline slash left-parenthesis q slash 2 plus 1 right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>C<\/mml:mi>\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>q<\/mml:mi>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">C_q = 2^{q\/2}\/(q\/2+1)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q\">\n                        <mml:semantics>\n                          <mml:mi>q<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">q<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    even and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q less-than-or-slanted-equals 52\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo>\n                              \u2a7d\n                              \n                            <\/mml:mo>\n                            <mml:mn>52<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">q\\leqslant 52<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Now for every integer\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script l greater-than-or-slanted-equals 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u2113\n                              \n                            <\/mml:mi>\n                            <mml:mo>\n                              \u2a7e\n                              \n                            <\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\ell \\geqslant 2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    there exists a sequence of generalized Rudin\u2013Shapiro polynomials, denoted by\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper P Subscript 0 comma n Superscript left-parenthesis script l right-parenthesis Baseline left-parenthesis z right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msubsup>\n                              <mml:mi>P<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>0<\/mml:mn>\n                                <mml:mo>,<\/mml:mo>\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                <mml:mi>\n                                  \u2113\n                                  \n                                <\/mml:mi>\n                                <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:msubsup>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>z<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">P_{0,n}^{(\\ell )}(z)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . In this paper, we extend our earlier method to these polynomials. In particular, the moments\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper M Subscript q Baseline left-parenthesis upper P Subscript 0 comma n Superscript left-parenthesis script l right-parenthesis Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msubsup>\n                              <mml:mi>P<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>0<\/mml:mn>\n                                <mml:mo>,<\/mml:mo>\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                <mml:mi>\n                                  \u2113\n                                  \n                                <\/mml:mi>\n                                <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:msubsup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathcal {M}_q(P_{0,n}^{(\\ell )})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    have been completely determined for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script l equals 3\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u2113\n                              \n                            <\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>3<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\ell =3<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q equals 4\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>4<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">q=4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , 6, 8, 10, for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script l equals 4\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u2113\n                              \n                            <\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>4<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\ell =4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q equals 4\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>4<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">q=4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , 6 and for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script l equals 5\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u2113\n                              \n                            <\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>5<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\ell = 5<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , 6, 7, 8 and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q equals 4\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>4<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">q=4<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . For higher values of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script l\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u2113\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\ell<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"q\">\n                        <mml:semantics>\n                          <mml:mi>q<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">q<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , we formulate a natural conjecture, which implies that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper M Subscript q Baseline left-parenthesis upper P Subscript 0 comma n Superscript left-parenthesis script l right-parenthesis Baseline right-parenthesis tilde upper C Subscript script l comma q Baseline script l Superscript n q slash 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msubsup>\n                              <mml:mi>P<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>0<\/mml:mn>\n                                <mml:mo>,<\/mml:mo>\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                <mml:mi>\n                                  \u2113\n                                  \n                                <\/mml:mi>\n                                <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:msubsup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>\n                              \u223c\n                              \n                            <\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>C<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>\n                                  \u2113\n                                  \n                                <\/mml:mi>\n                                <mml:mo>,<\/mml:mo>\n                                <mml:mi>q<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:msup>\n                              <mml:mi>\n                                \u2113\n                                \n                              <\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>n<\/mml:mi>\n                                <mml:mi>q<\/mml:mi>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathcal {M}_q(P_{0,n}^{(\\ell )})\\sim C_{\\ell ,q}\\ell ^{nq\/2}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , where\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C Subscript script l comma q\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>C<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>\n                                \u2113\n                                \n                              <\/mml:mi>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">C_{\\ell ,q}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is an explicit constant.\n                  <\/p>","DOI":"10.1090\/s0025-5718-05-01736-9","type":"journal-article","created":{"date-parts":[[2005,8,10]],"date-time":"2005-08-10T10:23:21Z","timestamp":1123669401000},"page":"1923-1935","source":"Crossref","is-referenced-by-count":6,"title":["Even moments of generalized Rudin\u2013Shapiro polynomials"],"prefix":"10.1090","volume":"74","author":[{"given":"Christophe","family":"Doche","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2005,3,15]]},"reference":[{"key":"1","unstructured":"C. Batut, K. Belabas, D. Bernardi, H. Cohen and M. Olivier, User\u2019s guide to PARI\/GP, ver. 2.1.3, 2002. http:\/\/www.parigp-home.de\/"},{"key":"2","doi-asserted-by":"crossref","unstructured":"C. Doche and L. Habsieger, Moments of the Rudin\u2013Shapiro polynomials. Journal of Fourier Analysis and Applications 10 (2004).","DOI":"10.1007\/s00041-004-3049-y"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1006\/jcta.1996.0038","article-title":"On integral zeros of Krawtchouk polynomials","volume":"74","author":"Krasikov, Ilia","year":"1996","journal-title":"J. Combin. Theory Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0097-3165","issn-type":"print"},{"issue":"2","key":"4","first-page":"145","article-title":"Some properties of generalized Rudin-Shapiro polynomials","volume":"12","author":"Lei, Zhi Xian","year":"1991","journal-title":"Chinese Ann. Math. Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/1000-8314","issn-type":"print"},{"key":"5","volume-title":"Some problems in real and complex analysis","author":"Littlewood, John E.","year":"1968"},{"key":"6","unstructured":"A GP\u2013PARI program to compute the moments of some generalized Rudin\u2013Shapiro polynomials. \\url{http:\/\/www.math.u-bordeaux.fr\/ cdoche\/moments.gp}"},{"key":"7","unstructured":"B. Saffari, personal communication, (2001)."},{"key":"8","unstructured":"H. S. Shapiro, Extremal problems for polynomials and power series, Ph.D. thesis, MIT, 1951."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01736-9\/S0025-5718-05-01736-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01736-9\/S0025-5718-05-01736-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:30:43Z","timestamp":1776781843000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01736-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3,15]]},"references-count":8,"journal-issue":{"issue":"252","published-print":{"date-parts":[[2005,10]]}},"alternative-id":["S0025-5718-05-01736-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-05-01736-9","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2005,3,15]]}}}