A variation of Euler's approach to values of the Riemann zeta function

2002/06/30 by Masanobu Kaneko, Nobushige Kurokawa, Masato Wakayama
Mathematics · #math.QA #math.NT #msc:11M06 #msc:11B65

paper · pdf

published as Kyushu Journal of Mathematics, Vol.57 No.1, 2003, 175--192 · 14 pages

arxiv created 2002/07/31 · arxiv updated 2009/11/30

Abstract

An elementary method of computing the values at negative integers of the Riemann zeta function is presented. The principal ingredient is a new q-analogue of the Riemann zeta function. We show that for any argument other than 1 the classical limit of this q-analogue exists and equals the value of the Riemann zeta.

Related

• A q-analogue for Euler's evaluations of the Riemann zeta function
• An elementary and real approach to values of the Riemann zeta function
• Calculating zeros of a q-zeta function numerically
• q-Euler Numbers and Polynomials Associated with Basic Zeta Functions
• Riemann Zeta Function. An Attempt to fathom Zeta(3)