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 On a $p$-adic analogue of $k$-ple Riemann zeta function Bull. Korean Math. Soc. 2012 Vol. 49, No. 1, 165-174 https://doi.org/10.4134/BKMS.2012.49.1.165Published online January 1, 2012 Daekil Park and Jin-Woo Son Kyungnam University, Kyungnam University Abstract : 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 Downloads: Full-text PDF