{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:56:28Z","timestamp":1774626988247,"version":"3.50.1"},"reference-count":16,"publisher":"American Mathematical Society (AMS)","issue":"242","license":[{"start":{"date-parts":[[2003,6,25]],"date-time":"2003-06-25T00:00:00Z","timestamp":1056499200000},"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>In this paper we give a general theorem on the linear independence measure of logarithms of rational numbers and, in particular, the linear independence measure of <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1 comma log 2 comma log 3 comma log 5\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mn>1<\/mml:mn>\n      <mml:mo>,<\/mml:mo>\n      <mml:mi>log<\/mml:mi>\n      <mml:mo>\u2061<\/mml:mo>\n      <mml:mn>2<\/mml:mn>\n      <mml:mo>,<\/mml:mo>\n      <mml:mi>log<\/mml:mi>\n      <mml:mo>\u2061<\/mml:mo>\n      <mml:mn>3<\/mml:mn>\n      <mml:mo>,<\/mml:mo>\n      <mml:mi>log<\/mml:mi>\n      <mml:mo>\u2061<\/mml:mo>\n      <mml:mn>5<\/mml:mn>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">1,\\log 2, \\log 3, \\log 5<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> and of <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1 comma log 2 comma log 3 comma log 5 comma log 7\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mn>1<\/mml:mn>\n      <mml:mo>,<\/mml:mo>\n      <mml:mi>log<\/mml:mi>\n      <mml:mo>\u2061<\/mml:mo>\n      <mml:mn>2<\/mml:mn>\n      <mml:mo>,<\/mml:mo>\n      <mml:mi>log<\/mml:mi>\n      <mml:mo>\u2061<\/mml:mo>\n      <mml:mn>3<\/mml:mn>\n      <mml:mo>,<\/mml:mo>\n      <mml:mi>log<\/mml:mi>\n      <mml:mo>\u2061<\/mml:mo>\n      <mml:mn>5<\/mml:mn>\n      <mml:mo>,<\/mml:mo>\n      <mml:mi>log<\/mml:mi>\n      <mml:mo>\u2061<\/mml:mo>\n      <mml:mn>7<\/mml:mn>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">1,\\log 2, \\log 3, \\log 5, \\log 7<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>. We also give a method to search for polynomials of smallest norm on a real interval <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-bracket a comma b right-bracket\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mo stretchy=\"false\">[<\/mml:mo>\n      <mml:mi>a<\/mml:mi>\n      <mml:mo>,<\/mml:mo>\n      <mml:mi>b<\/mml:mi>\n      <mml:mo stretchy=\"false\">]<\/mml:mo>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">[a,b]<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> which may be suitable for computing or improving the linear independence measure of logarithms of rational numbers.<\/p>","DOI":"10.1090\/s0025-5718-02-01442-4","type":"journal-article","created":{"date-parts":[[2003,2,10]],"date-time":"2003-02-10T16:10:52Z","timestamp":1044893452000},"page":"901-911","source":"Crossref","is-referenced-by-count":36,"title":["On the linear independence measure of logarithms of rational numbers"],"prefix":"10.1090","volume":"72","author":[{"given":"Qiang","family":"Wu","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2002,6,25]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"crossref","first-page":"885","DOI":"10.5802\/aif.1240","article-title":"Sur le diam\u00e8tre transfini entier d\u2019un intervalle r\u00e9el","volume":"40","author":"Amoroso, Francesco","year":"1990","journal-title":"Ann. 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