A VARIATION OF EULER′S APPROACH TO VALUES OF THE RIEMANN ZETA FUNCTION

2003/01/01 by Masanobu Kaneko, Nobushige Kurokawa, Masato Wakayama · 79 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematics and Applications #Mathematics #Particular values of Riemann zeta function #Riemann zeta function #Proof of the Euler product formula for the Riemann zeta function #Riemann hypothesis #Riemann Xi function #Arithmetic zeta function #Euler's formula #Pure mathematics #Function (biology) #Prime zeta function #Mathematical analysis #Mathematical physics

paper · pdf · doi:10.2206/kyushujm.57.175

published in Kyushu Journal of Mathematics 57(1), 175-192 (Kyushu University)

openalex publication_date 2003/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

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.

Citations

• Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung
• A course of modern analysis an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions

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