Revisiting the Riemann Zeta function at positive even integers

被引：2

作者：

Alladi, Krishnaswami ^{[1
]}

Defant, Colin ^{[2
]}

机构：

[1] Univ Florida, Dept Math, Gainesville, FL 32611 USA

[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

关键词：

Riemann zeta function; even positive integers; Euler's formula; Parseval identity; Bernoulli numbers;

D O I：

10.1142/S1793042118501105

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using Parseval's identity for the Fourier coefficients of xk, we provide a new proof that zeta(2k) = (-1)B-k+1(2k) (2 pi)(2k)/2(2k)!

引用

页码：1849 / 1856

页数：8

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