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北航数学论坛 On the decimal expansion of log(2018/2017) and e

发布日期:2018-04-16  |  浏览量:  
 报告人:Prof. Yann Bugeaud
 报告人单位:法国斯特拉斯堡大学(University of Strasbourg)
 报告时间:2018.4.23 下午4:00-5:00
 报告地点:(老)主楼321
 摘要:Let ξ be an irrational real number. Its irrationality exponent, denoted by µ(ξ), is the supremum of the real numbers µ for which there are infinitely many integer pairs (p, q) such that |ξ − p q | < q−µ. We always have µ(ξ) ≥ 2, with equality for almost all real numbers and for irrational algebraic numbers (by Roth’s theorem). We prove that, if the irrationality exponent of ξ is equal to 2 or slightly greater than 2, then the decimal expansion of ξ cannot be ‘too simple’, in a suitable sense. Our result applies, among other classical numbers, to badly approximable numbers, non-zero rational powers of e, and log(1 + 1 a ), provided that the integer a is sufficiently large. It establishes an unexpected connection between the irrationality exponent of a real number and its decimal expansion.
 报告人简介:Yann Bugeaud现为法国特斯拉斯堡大学教授,法国高等数 学研究所所长(Institut de Recherche Mathématique Avancée, UMR 7501), 是多个国际期刊的编委。他的主要研究方向包括丢番图逼近,超越数,模1分 布,丢番图方程,包括在顶尖期刊Annals of Math.等发表了180多篇学术论 文,他还出版过4本学术专刊(《Approximation by algebraic numbers》, 《Distribution modulo one and Diophantine approximation》,《Linear forms in logarithms and applications》和《The problem of Catalan》(与Yu. Bilu, M.Mignotte 合著)。
 邀请人: 郑志勇教授