On the distribution of multiples of real numbers

被引：0
|
作者：
Tanguy Rivoal
机构：
[1] Institut Fourier,
[2] CNRS UMR 5582,undefined
[3] Université Grenoble 1,undefined
[4] Université de Lyon,undefined
[5] CNRS et Université Lyon 1,undefined
[6] Institut Camille Jordan,undefined
[7] Bâtiment Braconnier,undefined
来源：
Monatshefte für Mathematik | 2011年 / 164卷
关键词：
Diophantine approximation; Lagrange spectrum; Continued fractions; Fourier series; Primary 11K60; Secondary 11J06; 11K70; 42A16;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We introduce new series (of the variable α) that enable to measure the irregularity of distribution of the sequence of fractional parts {nα}. A detailed analysis of the convergence and divergence of these series is done, depending mainly on the convergents of α. As a by product, we obtain new Fourier series of square integrable functions that converge almost everywhere but at no rational number.
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页码：325 / 360
页数：35
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