q -Riemann zeta function

Taekyun Kim

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-7

Abstract:

We consider the modified q -analogue of Riemann zeta function which is defined by ζ q ( s ) = ∑ n = 1 ∞ ( q n ( s − 1 ) / [ n ] s ) , 0 < q < 1 , s ∈ ℂ . In this paper, we give q -Bernoulli numbers which can be viewed as interpolation of the above q -analogue of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at negative integers. Also, we will treat some identities of q -Bernoulli numbers using nonarchimedean q -integration.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:165042

DOI: 10.1155/S0161171204307180

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