The author calls a uniformly differential function at ( for short) if the difference quotients, , have a limit as . Denote as usual , . Then for , the fermionic -adic invariant -integral on is defined as
Especially, one has
In the paper under review, the authors study certain integral equations related to from which they obtain several properties of Genocchi numbers and polynomials.
The main purpose is to derive the distribution relations of the Genocchi polynomials, and to construct the Genocchi zeta function which interpolates the Genocchi polynomials at negative integers.