{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:36:51Z","timestamp":1776785811305,"version":"3.51.2"},"reference-count":21,"publisher":"American Mathematical Society (AMS)","issue":"255","license":[{"start":{"date-parts":[[2007,3,28]],"date-time":"2007-03-28T00:00:00Z","timestamp":1175040000000},"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                    In this work, we show how suitable generalizations of the integer transfinite diameter of some compact sets in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper C\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi mathvariant=\"double-struck\">C<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {C}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    give very good bounds for coefficients of polynomials with small Mahler measure. By this way, we give the list of all monic irreducible primitive polynomials of\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 upper 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                    of degree at most\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"36\">\n                        <mml:semantics>\n                          <mml:mn>36<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">36<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with Mahler measure less than\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1 period 324 period period period\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>1.<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mn>324...<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">1.\\,324...<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and of degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"38\">\n                        <mml:semantics>\n                          <mml:mn>38<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">38<\/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=\"40\">\n                        <mml:semantics>\n                          <mml:mn>40<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">40<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with Mahler measure less than\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1 period 31\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>1.<\/mml:mn>\n                            <mml:mspace width=\"thinmathspace\"\/>\n                            <mml:mn>31<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">1.\\,31<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-06-01791-1","type":"journal-article","created":{"date-parts":[[2006,5,24]],"date-time":"2006-05-24T14:43:01Z","timestamp":1148481781000},"page":"1527-1540","source":"Crossref","is-referenced-by-count":17,"title":["Integer transfinite diameter and polynomials with small Mahler measure"],"prefix":"10.1090","volume":"75","author":[{"given":"Val\u00e9rie","family":"Flammang","sequence":"first","affiliation":[]},{"given":"Georges","family":"Rhin","sequence":"additional","affiliation":[]},{"given":"Jean-Marc","family":"Sac-\u00c9p\u00e9e","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2006,3,28]]},"reference":[{"key":"1","series-title":"CMS Books in Mathematics\/Ouvrages de Math\\'{e}matiques de la SMC","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21652-2","volume-title":"Computational 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