IRRATIONALITY OF gamma, zeta(m) AND beta(m)

被引：2

作者：

Gauthier, Claude ^{[1
]}

机构：

[1] Univ Moncton, Dept Math & Stat, Moncton, NB E1A 3E9, Canada

来源：

JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2015年 / 37卷 / 01期

关键词：

irrationality; Euler's constant; Riemann's zeta function; Dirichlet's beta function; Catalan's constant;

D O I：

10.17654/JPANTAAug2015_041_052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use the uniqueness of representation of every rational number as a finite sum of reciprocal factorials to any given power m is an element of N* to prove the irrationality of Euler's constant., of all values of Riemann's zeta function zeta(m), m >= 2, and of all values of Dirichlet's beta function beta(m), with beta(2) corresponding to Catalan's constant.

引用

页码：41 / 52

页数：12

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