{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:45:25Z","timestamp":1776840325059,"version":"3.51.2"},"reference-count":13,"publisher":"American Mathematical Society (AMS)","issue":"252","license":[{"start":{"date-parts":[[2006,3,8]],"date-time":"2006-03-08T00:00:00Z","timestamp":1141776000000},"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                    We find all\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"15909\">\n                        <mml:semantics>\n                          <mml:mn>15909<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">15909<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    algebraic integers\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"bold-italic alpha\">\n                        <mml:semantics>\n                          <mml:mi mathvariant=\"bold-italic\">\n                            \u03b1\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\boldsymbol {\\alpha }<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    whose conjugates all lie in an ellipse with two of them nonreal, while the others lie in the real interval\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-bracket negative 1 comma 2 right-bracket\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">[<\/mml:mo>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mo stretchy=\"false\">]<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">[-1,2]<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . This problem has applications to finding certain subgroups of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper S upper L left-parenthesis 2 comma double-struck upper C right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>S<\/mml:mi>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">C<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">SL(2,\\mathbb {C})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We use explicit auxiliary functions related to the generalized integer transfinite diameter of compact subsets of\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                    . This gives good bounds for the coefficients of the minimal polynomial of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"bold-italic alpha period\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"bold-italic\">\n                              \u03b1\n                              \n                            <\/mml:mi>\n                            <mml:mo>.<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\boldsymbol {\\alpha }.<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                  <\/p>","DOI":"10.1090\/s0025-5718-05-01735-7","type":"journal-article","created":{"date-parts":[[2005,8,10]],"date-time":"2005-08-10T10:23:21Z","timestamp":1123669401000},"page":"2007-2015","source":"Crossref","is-referenced-by-count":3,"title":["Algebraic integers whose conjugates all lie in an ellipse"],"prefix":"10.1090","volume":"74","author":[{"given":"Val\u00e9rie","family":"Flammang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Georges","family":"Rhin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2005,3,8]]},"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 excursions in analysis and number theory","volume":"10","author":"Borwein, Peter","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/0387954449"},{"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. 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