The classical Genocchi numbers, are defined by means of the following generating function: , where . Relations between Genocchi numbers, Bernoulli numbers and Euler polynomials are given by . Genocchi numbers and polynomials are very important not only in Number Theory but also in the other areas in Mathematics and Mathematical Physics. The authors define -Genocchi numbers and polynomials by means of the following generating functions, respectively:
where and with . The authors give interpolations functions of these numbers and polynomials at negative integers. They define -adic --function which interpolate -Genocchi numbers at negative integers. They also give congruences for -Genocchi numbers.