Journal of the
Korean Mathematical Society JKMS

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.

Keywords: $q$-Genocchi numbers, $p$-adic measures, $p$-adic integral, Kummer congruences

MSC numbers: Primary 11B68, 43A05, 11S80, 11A07