$q$-Extensions of Genocchi Numbers

다국어 초록 (Multilingual Abstract)

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.

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