On Some Arithmetical Properties of the Genocchi Numbers and Polynomials

We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function.We have the generating function of h, q -Genocchi polynomials. We define the Cangul-Ozden-Simsek’s type twisted h, q -Genocchi polynomials and numbers. We also have the generalized twisted h, q -Genocchi numbers attached to the Dirichlet’s character χ. Finally, we define zeta functions related to h, q -Genocchi polynomials and have the generating function of the generalized h, q -Genocchi numbers attached to χ.