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Bull. Korean Math. Soc. 2012; 49(1): 165-174

Printed January 1, 2012

https://doi.org/10.4134/BKMS.2012.49.1.165

Copyright © The Korean Mathematical Society.

On a $p$-adic analogue of $k$-ple Riemann zeta function

Daekil Park and Jin-Woo Son

Kyungnam University, Kyungnam University

Abstract

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In this paper, we construct a $p$-adic analogue of multiple Riemann zeta values and express their values at non-positive integers. In particular, we obtain a new congruence of the higher order Frobenius-Euler numbers and the Kummer congruences for the Bernoulli numbers as a corollary.

Keywords: $p$-adic analogues, higher order Frobenius-Euler numbers, $k$-ple zeta function, Kummer-type congruences

MSC numbers: 11B68, 11S80

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