{"title":"在交换代数群中对数的线性独立性的度量","authors":"Éric Gaudron","doi":"10.1016/S0764-4442(01)02190-5","DOIUrl":null,"url":null,"abstract":"<div><p>We obtain some new results in the theory of linear forms in logarithms on a commutative algebraic group, defined over <span><math><mtext>Q</mtext></math></span>. We generalize recent progress of S. David and N. Hirata [1]. In particular, we achieve an optimal linear independence measure in the height of the linear form and a measure more precise than Hirata's [4] for parameters related to the logarithms. The proof rests on Baker's method and a new argument of arithmetical nature.</p></div>","PeriodicalId":100300,"journal":{"name":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","volume":"333 12","pages":"Pages 1059-1064"},"PeriodicalIF":0.0000,"publicationDate":"2001-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02190-5","citationCount":"15","resultStr":"{\"title\":\"Mesure d'indépendance linéaire de logarithmes dans un groupe algébrique commutatif\",\"authors\":\"Éric Gaudron\",\"doi\":\"10.1016/S0764-4442(01)02190-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We obtain some new results in the theory of linear forms in logarithms on a commutative algebraic group, defined over <span><math><mtext>Q</mtext></math></span>. We generalize recent progress of S. David and N. Hirata [1]. In particular, we achieve an optimal linear independence measure in the height of the linear form and a measure more precise than Hirata's [4] for parameters related to the logarithms. The proof rests on Baker's method and a new argument of arithmetical nature.</p></div>\",\"PeriodicalId\":100300,\"journal\":{\"name\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"volume\":\"333 12\",\"pages\":\"Pages 1059-1064\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0764-4442(01)02190-5\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0764444201021905\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus de l'Académie des Sciences - Series I - Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0764444201021905","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mesure d'indépendance linéaire de logarithmes dans un groupe algébrique commutatif
We obtain some new results in the theory of linear forms in logarithms on a commutative algebraic group, defined over . We generalize recent progress of S. David and N. Hirata [1]. In particular, we achieve an optimal linear independence measure in the height of the linear form and a measure more precise than Hirata's [4] for parameters related to the logarithms. The proof rests on Baker's method and a new argument of arithmetical nature.
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