{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T15:31:57Z","timestamp":1776871917463,"version":"3.51.2"},"reference-count":29,"publisher":"American Mathematical Society (AMS)","issue":"331","license":[{"start":{"date-parts":[[2022,5,20]],"date-time":"2022-05-20T00:00:00Z","timestamp":1653004800000},"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                    The \u201cSchur-Siegel-Smyth trace problem\u201d is a famous open problem that has existed for nearly 100 years. To study this problem with the known methods, we need to find all totally positive algebraic integers with small trace. In this work, on the basis of the classical algorithm, we construct a new type of explicit auxiliary functions related to Chebyshev polynomials to give better bounds for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S Subscript k\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>S<\/mml:mi>\n                            <mml:mi>k<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">S_k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , and reduce sharply the computing time. We are then able to push the computation to degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"15\">\n                        <mml:semantics>\n                          <mml:mn>15<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">15<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and prove that there is no such totally positive algebraic integer with absolute trace\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1.8\">\n                        <mml:semantics>\n                          <mml:mn>1.8<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">1.8<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . As an application, we improve the lower bound for the absolute trace of totally positive algebraic integers to\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1.793145 midline-horizontal-ellipsis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>1.793145<\/mml:mn>\n                            <mml:mo>\n                              \u22ef\n                              \n                            <\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">1.793145\\cdots<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/mcom\/3636","type":"journal-article","created":{"date-parts":[[2021,1,27]],"date-time":"2021-01-27T14:31:22Z","timestamp":1611757882000},"page":"2317-2332","source":"Crossref","is-referenced-by-count":7,"title":["Totally positive algebraic integers with small trace"],"prefix":"10.1090","volume":"90","author":[{"given":"Cong","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2021,5,20]]},"reference":[{"issue":"253","key":"1","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1090\/S0025-5718-05-01776-X","article-title":"The trace of totally positive algebraic integers","volume":"75","author":"Aguirre, Juli\u00e1n","year":"2006","journal-title":"Math. 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