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2002•arXiv (Cornell University)Open access

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

Masanobu Kaneko, Nobushige Kurokawa, Masato Wakayama

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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.

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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.

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Available 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.

Key concepts: Particular values of Riemann zeta function, Proof of the Euler product formula for the Riemann zeta function, Riemann zeta function, Riemann Xi function, Riemann hypothesis, Mathematics, Arithmetic zeta function, Euler's formula

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