A few remarks on the values of the Bernoulli polynomials at rational arguments and some relations with ζ(2k

被引：1
|
作者：
de Camargo, Andre Pierro [1 ]
de Oliveira Teruya, Giulliano Cogui [1 ]
机构：
[1] Fed Univ ABC Reg, Santo Andre, SP, Brazil
来源：
NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | 2021年 / 27卷 / 04期
关键词：
Bernoulli polynomials; Bernoulli numbers; Riemann zeta function; Euler's formula; NUMBERS;
D O I：
10.7546/nntdm.2021.27.4.180-186
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A problem posed by Lehmer in 1938 asks for simple closed formulae for the values of the even Bernoulli polynomials at rational arguments in terms of the Bernoulli numbers. We discuss this problem based on the Fourier expansion of the Bernoulli polynomials. We also give some necessary and sufficient conditions for zeta(2k + 1) be a rational multiple of pi(2k+1.)
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页码：180 / 186
页数：7
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