{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:05:09Z","timestamp":1776801909383,"version":"3.51.2"},"reference-count":11,"publisher":"American Mathematical Society (AMS)","issue":"301","license":[{"start":{"date-parts":[[2016,11,20]],"date-time":"2016-11-20T00:00:00Z","timestamp":1479600000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001031","name":"Australian Respiratory Council","doi-asserted-by":"publisher","award":["DP130100237"],"award-info":[{"award-number":["DP130100237"]}],"id":[{"id":"10.13039\/501100001031","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001031","name":"Australian Respiratory Council","doi-asserted-by":"publisher","award":["DP140100118"],"award-info":[{"award-number":["DP140100118"]}],"id":[{"id":"10.13039\/501100001031","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    For the Gauss sums which are defined by\n                    <disp-formula content-type=\"math\/mathml\">\n                      \\[\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S Subscript n Baseline left-parenthesis a comma q right-parenthesis colon equals sigma-summation Underscript x mod q Endscripts bold e left-parenthesis a x Superscript n Baseline slash q right-parenthesis comma\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>S<\/mml:mi>\n                              <mml:mi>n<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>:=<\/mml:mo>\n                            <mml:munder>\n                              <mml:mo>\n                                \u2211\n                                \n                              <\/mml:mo>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>x<\/mml:mi>\n                                <mml:mo lspace=\"thickmathspace\" rspace=\"thickmathspace\">mod<\/mml:mo>\n                                <mml:mi>q<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:munder>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"bold\">e<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:msup>\n                              <mml:mi>x<\/mml:mi>\n                              <mml:mi>n<\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>,<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">S_n(a,q):=\\sum _{x\\bmod q}\\mathbf {e}(ax^n\/q),<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                      \\]\n                    <\/disp-formula>\n                    Stechkin\u00a0(1975) conjectured that the quantity\n                    <disp-formula content-type=\"math\/mathml\">\n                      \\[\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A colon equals sup Underscript n comma q greater-than-or-slanted-equals 2 Endscripts max Underscript gcd left-parenthesis a comma q right-parenthesis equals 1 Endscripts StartFraction StartAbsoluteValue upper S Subscript n Baseline left-parenthesis a comma q right-parenthesis EndAbsoluteValue Over q Superscript 1 minus 1 slash n Baseline EndFraction\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>A<\/mml:mi>\n                            <mml:mo>:=<\/mml:mo>\n                            <mml:munder>\n                              <mml:mo movablelimits=\"true\" form=\"prefix\">sup<\/mml:mo>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>n<\/mml:mi>\n                                <mml:mo>,<\/mml:mo>\n                                <mml:mi>q<\/mml:mi>\n                                <mml:mo>\n                                  \u2a7e\n                                  \n                                <\/mml:mo>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:munder>\n                            <mml:mtext>\u00a0<\/mml:mtext>\n                            <mml:munder>\n                              <mml:mo movablelimits=\"true\" form=\"prefix\">max<\/mml:mo>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo movablelimits=\"true\" form=\"prefix\">gcd<\/mml:mo>\n                                <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                <mml:mi>a<\/mml:mi>\n                                <mml:mo>,<\/mml:mo>\n                                <mml:mi>q<\/mml:mi>\n                                <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                <mml:mo>=<\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:munder>\n                            <mml:mfrac>\n                              <mml:mrow>\n                                <mml:mstyle scriptlevel=\"0\">\n                                  <mml:mrow class=\"MJX-TeXAtom-OPEN\">\n                                    <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">|<\/mml:mo>\n                                  <\/mml:mrow>\n                                <\/mml:mstyle>\n                                <mml:msub>\n                                  <mml:mi>S<\/mml:mi>\n                                  <mml:mi>n<\/mml:mi>\n                                <\/mml:msub>\n                                <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                <mml:mi>a<\/mml:mi>\n                                <mml:mo>,<\/mml:mo>\n                                <mml:mi>q<\/mml:mi>\n                                <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                <mml:mstyle scriptlevel=\"0\">\n                                  <mml:mrow class=\"MJX-TeXAtom-CLOSE\">\n                                    <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">|<\/mml:mo>\n                                  <\/mml:mrow>\n                                <\/mml:mstyle>\n                              <\/mml:mrow>\n                              <mml:msup>\n                                <mml:mi>q<\/mml:mi>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mn>1<\/mml:mn>\n                                  <mml:mo>\n                                    \u2212\n                                    \n                                  <\/mml:mo>\n                                  <mml:mn>1<\/mml:mn>\n                                  <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                    <mml:mo>\/<\/mml:mo>\n                                  <\/mml:mrow>\n                                  <mml:mi>n<\/mml:mi>\n                                <\/mml:mrow>\n                              <\/mml:msup>\n                            <\/mml:mfrac>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">A:=\\sup _{n,q\\geqslant 2}~\\max _{\\gcd (a,q)=1}\\frac {\\bigl |S_n(a,q)\\bigr |}{q^{1-1\/n}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                      \\]\n                    <\/disp-formula>\n                    is finite. Shparlinski\u00a0 (1991) proved that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A\">\n                        <mml:semantics>\n                          <mml:mi>A<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">A<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is finite, but in the absence of effective bounds on the sums\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S Subscript n Baseline left-parenthesis a comma q right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>S<\/mml:mi>\n                              <mml:mi>n<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">S_n(a,q)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    the precise determination of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A\">\n                        <mml:semantics>\n                          <mml:mi>A<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">A<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    has remained intractable for many years. Using recent work of Cochrane and Pinner\u00a0(2011) on Gauss sums with prime moduli, in this paper we show that with the constant given by\n                    <disp-formula content-type=\"math\/mathml\">\n                      \\[\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A equals StartAbsoluteValue upper S 6 left-parenthesis ModifyingAbove a With caret comma ModifyingAbove q With caret right-parenthesis EndAbsoluteValue slash ModifyingAbove q With caret Superscript 1 minus 1 slash 6 Baseline equals 4.709236 ellipsis comma\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>A<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mstyle scriptlevel=\"0\">\n                              <mml:mrow class=\"MJX-TeXAtom-OPEN\">\n                                <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">|<\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:mstyle>\n                            <mml:msub>\n                              <mml:mi>S<\/mml:mi>\n                              <mml:mn>6<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mover>\n                                <mml:mi>a<\/mml:mi>\n                                <mml:mo stretchy=\"false\">\n                                  ^\n                                  \n                                <\/mml:mo>\n                              <\/mml:mover>\n                            <\/mml:mrow>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mover>\n                                <mml:mi>q<\/mml:mi>\n                                <mml:mo stretchy=\"false\">\n                                  ^\n                                  \n                                <\/mml:mo>\n                              <\/mml:mover>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mstyle scriptlevel=\"0\">\n                              <mml:mrow class=\"MJX-TeXAtom-CLOSE\">\n                                <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">|<\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:mstyle>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:msup>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mover>\n                                  <mml:mi>q<\/mml:mi>\n                                  <mml:mo stretchy=\"false\">\n                                    ^\n                                    \n                                  <\/mml:mo>\n                                <\/mml:mover>\n                              <\/mml:mrow>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mo>\n                                  \u2212\n                                  \n                                <\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mn>6<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>4.709236<\/mml:mn>\n                            <mml:mo>\n                              \u2026\n                              \n                            <\/mml:mo>\n                            <mml:mo>,<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">A=\\bigl |S_6(\\hat a,\\hat q)\\bigr |\/\\hat q^{1-1\/6}=4.709236\\ldots ,<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                      \\]\n                    <\/disp-formula>\n                    where\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"ModifyingAbove a With caret colon equals 4787\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mover>\n                                <mml:mi>a<\/mml:mi>\n                                <mml:mo stretchy=\"false\">\n                                  ^\n                                  \n                                <\/mml:mo>\n                              <\/mml:mover>\n                            <\/mml:mrow>\n                            <mml:mo>:=<\/mml:mo>\n                            <mml:mn>4787<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\hat a:=4787<\/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=\"ModifyingAbove q With caret colon equals 4606056 equals 2 cubed dot 3 squared dot 7 dot 13 dot 19 dot 37\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mover>\n                                <mml:mi>q<\/mml:mi>\n                                <mml:mo stretchy=\"false\">\n                                  ^\n                                  \n                                <\/mml:mo>\n                              <\/mml:mover>\n                            <\/mml:mrow>\n                            <mml:mo>:=<\/mml:mo>\n                            <mml:mn>4606056<\/mml:mn>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:msup>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mn>3<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\n                                \u22c5\n                                \n                              <\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:msup>\n                              <mml:mn>3<\/mml:mn>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\n                                \u22c5\n                                \n                              <\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mn>7<\/mml:mn>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\n                                \u22c5\n                                \n                              <\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mn>13<\/mml:mn>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\n                                \u22c5\n                                \n                              <\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mn>19<\/mml:mn>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\n                                \u22c5\n                                \n                              <\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mn>37<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\hat q:=4606056=2^3{\\cdot }3^2{\\cdot }7{\\cdot }13{\\cdot }19{\\cdot }37<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , one has the sharp inequality\n                    <disp-formula content-type=\"math\/mathml\">\n                      \\[\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"StartAbsoluteValue upper S Subscript n Baseline left-parenthesis a comma q right-parenthesis EndAbsoluteValue less-than-or-slanted-equals upper A q Superscript 1 minus 1 slash n\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mstyle scriptlevel=\"0\">\n                              <mml:mrow class=\"MJX-TeXAtom-OPEN\">\n                                <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">|<\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:mstyle>\n                            <mml:msub>\n                              <mml:mi>S<\/mml:mi>\n                              <mml:mi>n<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mstyle scriptlevel=\"0\">\n                              <mml:mrow class=\"MJX-TeXAtom-CLOSE\">\n                                <mml:mo maxsize=\"1.2em\" minsize=\"1.2em\">|<\/mml:mo>\n                              <\/mml:mrow>\n                            <\/mml:mstyle>\n                            <mml:mo>\n                              \u2a7d\n                              \n                            <\/mml:mo>\n                            <mml:mi>A<\/mml:mi>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:msup>\n                              <mml:mi>q<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mo>\n                                  \u2212\n                                  \n                                <\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mi>n<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\bigl |S_n(a,q)\\bigr |\\leqslant A\\,q^{1-1\/n}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                      \\]\n                    <\/disp-formula>\n                    for all\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n comma q greater-than-or-slanted-equals 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>q<\/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\">n,q\\geqslant 2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and all\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"a element-of double-struck upper Z\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>\n                              \u2208\n                              \n                            <\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Z<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">a\\in \\mathbb {Z}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"gcd left-parenthesis a comma q right-parenthesis equals 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo movablelimits=\"true\" form=\"prefix\">gcd<\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\gcd (a,q)=1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . One interesting aspect of our method is that we apply effective lower bounds for the center density in the sphere packing problem due to Cohn and Elkies\u00a0(2003) to derive new effective bounds on the sums\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S Subscript n Baseline left-parenthesis a comma q right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>S<\/mml:mi>\n                              <mml:mi>n<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">S_n(a,q)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in order to make the task computationally feasible.\n                  <\/p>","DOI":"10.1090\/mcom3056","type":"journal-article","created":{"date-parts":[[2015,3,25]],"date-time":"2015-03-25T14:30:50Z","timestamp":1427293850000},"page":"2569-2581","source":"Crossref","is-referenced-by-count":2,"title":["On Gauss sums and the evaluation of Stechkin\u2019s constant"],"prefix":"10.1090","volume":"85","author":[{"given":"William","family":"Banks","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Igor","family":"Shparlinski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,11,20]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1093\/qmath\/hap041","article-title":"Explicit bounds on monomial and binomial exponential sums","volume":"62","author":"Cochrane, Todd","year":"2011","journal-title":"Q. 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