{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T15:31:54Z","timestamp":1776871914263,"version":"3.51.2"},"reference-count":9,"publisher":"American Mathematical Society (AMS)","issue":"253","license":[{"start":{"date-parts":[[2006,9,12]],"date-time":"2006-09-12T00:00:00Z","timestamp":1158019200000},"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 all totally positive algebraic numbers\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                    except a finite number of explicit exceptions, the following inequality holds:\n                    <disp-formula content-type=\"math\/mathml\">\n                      \\[\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"StartFraction 1 Over d EndFraction left-parenthesis alpha 1 plus midline-horizontal-ellipsis plus alpha Subscript d Baseline right-parenthesis greater-than max left-parenthesis 1.780022 comma 1.66 plus alpha 1 right-parenthesis comma\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mfrac>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mi>d<\/mml:mi>\n                            <\/mml:mfrac>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mo>\n                              \u22ef\n                              \n                            <\/mml:mo>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                              <mml:mi>d<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mo movablelimits=\"true\" form=\"prefix\">max<\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>1.780022<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>1.66<\/mml:mn>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>,<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\frac {1}{d}\\,(\\alpha _1+\\dots +\\alpha _d)&gt;\\max (1.780022,1.66+\\alpha _1),<\/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=\"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                    is the degree 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                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"0 greater-than alpha 1 greater-than midline-horizontal-ellipsis greater-than alpha Subscript d\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>0<\/mml:mn>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mo>\n                              \u22ef\n                              \n                            <\/mml:mo>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                              <mml:mi>d<\/mml:mi>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">0&gt;\\alpha _1&gt;\\dots &gt;\\alpha _d<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    its conjugates. This improves previous results of Smyth, Flammang and Rhin.\n                  <\/p>","DOI":"10.1090\/s0025-5718-05-01776-x","type":"journal-article","created":{"date-parts":[[2005,11,16]],"date-time":"2005-11-16T10:22:35Z","timestamp":1132136555000},"page":"385-393","source":"Crossref","is-referenced-by-count":14,"title":["The trace of totally positive algebraic integers"],"prefix":"10.1090","volume":"75","author":[{"given":"Juli\u00e1n","family":"Aguirre","sequence":"first","affiliation":[]},{"given":"Mikel","family":"Bilbao","sequence":"additional","affiliation":[]},{"given":"Juan","family":"Peral","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2005,9,12]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/0021-9045(88)90093-7","article-title":"On the asymptotic structure of the polynomials of minimal Diophantic deviation from zero","volume":"55","author":"Aparicio Bernardo, Emiliano","year":"1988","journal-title":"J. Approx. Theory","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9045","issn-type":"print"},{"issue":"214","key":"2","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1090\/S0025-5718-96-00702-8","article-title":"The integer Chebyshev problem","volume":"65","author":"Borwein, Peter","year":"1996","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"137","DOI":"10.5802\/jtnb.193","article-title":"The integer transfinite diameter of intervals and totally real algebraic integers","volume":"9","author":"Flammang, V.","year":"1997","journal-title":"J. Th\\'{e}or. 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