• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.183-198
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• 2006

In this paper q-extensions of Genocchi numbers are defined and several properties of these numbers are presented. Properties of q-Genocchi numbers and polynomials are used to construct q-extensions of p-adic measures which yield to obtain p-adic interpolation functions for q-Genocchi numbers. As an application, general systems of congruences, including Kummer-type congruences for q-Genocchi numbers are proved.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.391-410
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• 2000

In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.79-82
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• 1993

We let F be a p-adic field with ring of integers O. Suppose .THETA.$_{i}$ .mem. $F^{x}$ /( $F^{x}$ )$^{2}$ for i=1,2 and write $E^{{\theta}_{i}}$:= F(.root..THETA.$_{i}$ ). Then there appear some specific sets such as ( $E^{{\theta}_{i}}$)$^{x}$ / $F^{x}$ in [1] which we need to measure. In addition to that, nanother possible condition attached to the generalized results in [2] had better be presented even though they may not be quite so important. This paper is concerned with these matters. Most notations and conventions are standard and have been used also in [1] and [2].