On the von Staudt–Clausen’s theorem associated with q-Genocchi numbers

Abstract

Recently, the von Staudt–Clausen’s theorem for q-Euler numbers was introduced by Kim (2013) andq-Genocchi numbers were constructed by Araci et al. (2013). In this paper, we give the corresponding von Staudt–Clausen’s theorem for q-Genocchi numbers and also get the Kummer-type congruence for q-Genocchi numbers.