{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:47:04Z","timestamp":1776728824487,"version":"3.51.2"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"243","license":[{"start":{"date-parts":[[2003,12,6]],"date-time":"2003-12-06T00:00:00Z","timestamp":1070668800000},"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                    For\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper A Subscript t Baseline left-parenthesis x right-parenthesis equals f left-parenthesis x right-parenthesis minus t g left-parenthesis x right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>A<\/mml:mi>\n                              <mml:mi>t<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mi>f<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mi>g<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">A_t(x) = f(x) - t\\, g(x)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , we consider the set\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"StartSet sigma-summation Underscript upper A Subscript t Baseline left-parenthesis alpha right-parenthesis equals 0 Endscripts h left-parenthesis alpha right-parenthesis colon t element-of double-struck upper Q overbar EndSet\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo fence=\"false\" stretchy=\"false\">{<\/mml:mo>\n                            <mml:munder>\n                              <mml:mo>\n                                \u2211\n                                \n                              <\/mml:mo>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:msub>\n                                  <mml:mi>A<\/mml:mi>\n                                  <mml:mi>t<\/mml:mi>\n                                <\/mml:msub>\n                                <mml:mo stretchy=\"false\">(<\/mml:mo>\n                                <mml:mi>\n                                  \u03b1\n                                  \n                                <\/mml:mi>\n                                <mml:mo stretchy=\"false\">)<\/mml:mo>\n                                <mml:mo>=<\/mml:mo>\n                                <mml:mn>0<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:munder>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>\n                              \u03b1\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>:<\/mml:mo>\n                            <mml:mi>t<\/mml:mi>\n                            <mml:mo>\n                              \u2208\n                              \n                            <\/mml:mo>\n                            <mml:mover>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"double-struck\">Q<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mo accent=\"false\">\n                                \u00af\n                                \n                              <\/mml:mo>\n                            <\/mml:mover>\n                            <mml:mo fence=\"false\" stretchy=\"false\">}<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\{ \\sum _{A_t(\\alpha ) = 0} h(\\alpha ) : t \\in \\overline {\\mathbb {Q}} \\}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The polynomials\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"f left-parenthesis x right-parenthesis comma g left-parenthesis x right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>f<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>g<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">f(x), g(x)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper Z left-bracket x right-bracket\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">Z<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">[<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">]<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {Z}[x]<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , with only mild restrictions, and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h left-parenthesis alpha right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>\n                              \u03b1\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">h(\\alpha )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is the Weil height of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"alpha\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03b1\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\alpha<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We show that this set is dense in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-bracket d comma normal infinity right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">[<\/mml:mo>\n                            <mml:mi>d<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi mathvariant=\"normal\">\n                              \u221e\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">[d, \\infty )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for some effectively computable limit point\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"d\">\n                        <mml:semantics>\n                          <mml:mi>d<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">d<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-02-01481-3","type":"journal-article","created":{"date-parts":[[2003,4,18]],"date-time":"2003-04-18T13:09:02Z","timestamp":1050671342000},"page":"1487-1499","source":"Crossref","is-referenced-by-count":1,"title":["Sums of heights of algebraic numbers"],"prefix":"10.1090","volume":"72","author":[{"given":"Gregory","family":"Dresden","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2002,12,6]]},"reference":[{"key":"1","isbn-type":"print","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1090\/crmp\/019\/03","article-title":"The operator \ud835\udc65+(1\/\ud835\udc65)-2 and the reciprocal integers","author":"Bertin, M.-J.","year":"1999","ISBN":"https:\/\/id.crossref.org\/isbn\/0821809644"},{"issue":"2","key":"2","first-page":"211","article-title":"Effective measures of irrationality for cubic extensions of number fields","volume":"23","author":"Bombieri, E.","year":"1996","journal-title":"Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)","ISSN":"https:\/\/id.crossref.org\/issn\/0391-173X","issn-type":"print"},{"issue":"233","key":"3","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1090\/S0025-5718-00-01183-2","article-title":"On the spectrum of the Zhang-Zagier height","volume":"70","author":"Doche, Christophe","year":"2001","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"4","doi-asserted-by":"publisher","first-page":"103","DOI":"10.5802\/jtnb.307","article-title":"Zhang-Zagier heights of perturbed polynomials","volume":"13","author":"Doche, Christophe","year":"2001","journal-title":"J. Th\\'{e}or. Nombres Bordeaux","ISSN":"https:\/\/id.crossref.org\/issn\/1246-7405","issn-type":"print"},{"key":"5","unstructured":"G. Dresden, Spectra of heights over certain finite groups, Ph.D. thesis, The University of Texas at Austin, August 1997."},{"issue":"222","key":"6","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1090\/S0025-5718-98-00963-6","article-title":"Orbits of algebraic numbers with low heights","volume":"67","author":"Dresden, Gregory P.","year":"1998","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"7","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1006\/jnth.1995.1101","article-title":"Sur la longueur des entiers alg\u00e9briques totalement positifs","volume":"54","author":"Flammang, V.","year":"1995","journal-title":"J. Number Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0022-314X","issn-type":"print"},{"issue":"213","key":"8","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1090\/S0025-5718-96-00664-3","article-title":"Two new points in the spectrum of the absolute Mahler measure of totally positive algebraic integers","volume":"65","author":"Flammang, V.","year":"1996","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"9","doi-asserted-by":"publisher","first-page":"239","DOI":"10.4064\/aa-79-3-239-247","article-title":"On the Mahler measure of the composition of two polynomials","volume":"79","author":"Rhin, G.","year":"1997","journal-title":"Acta Arith.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"key":"10","first-page":"373","article-title":"Sur certaines s\u00e9ries de Taylor admettant leur cercle de convergence comme coupure essentielle","volume":"209","author":"Denjoy, Arnaud","year":"1939","journal-title":"C. R. Acad. Sci. Paris","ISSN":"https:\/\/id.crossref.org\/issn\/0001-4036","issn-type":"print"},{"issue":"2","key":"11","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1017\/S1446788700016426","article-title":"On the measure of totally real algebraic integers","volume":"30","author":"Smyth, C. J.","year":"1980","journal-title":"J. Austral. Math. Soc. Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0263-6115","issn-type":"print"},{"issue":"2","key":"12","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1017\/S1446788700016426","article-title":"On the measure of totally real algebraic integers","volume":"30","author":"Smyth, C. J.","year":"1980","journal-title":"J. Austral. Math. Soc. Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0263-6115","issn-type":"print"},{"key":"13","series-title":"American Mathematical Society Colloquium Publications, Vol. XXIII","volume-title":"Orthogonal polynomials","author":"Szeg\u0151, G\u00e1bor","year":"1975","edition":"4"},{"issue":"203","key":"14","doi-asserted-by":"publisher","first-page":"485","DOI":"10.2307\/2152970","article-title":"Algebraic numbers close to both 0 and 1","volume":"61","author":"Zagier, D.","year":"1993","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"15","doi-asserted-by":"publisher","first-page":"569","DOI":"10.2307\/2946601","article-title":"Positive line bundles on arithmetic surfaces","volume":"136","author":"Zhang, Shouwu","year":"1992","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2003-72-243\/S0025-5718-02-01481-3\/S0025-5718-02-01481-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2003-72-243\/S0025-5718-02-01481-3\/S0025-5718-02-01481-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:20:58Z","timestamp":1776727258000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2003-72-243\/S0025-5718-02-01481-3\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12,6]]},"references-count":15,"journal-issue":{"issue":"243","published-print":{"date-parts":[[2003,7]]}},"alternative-id":["S0025-5718-02-01481-3"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-02-01481-3","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":[[2002,12,6]]}}}