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On interpolation functions of the twisted generalized Frobenius-Euler numbers. (English) Zbl 1217.11115
Summary: The main purpose of this paper is to apply the Mellin transform to the generating functions of $q$-generalized Frobenius-Euler numbers and twisted $q$-generalized Frobenius-Euler numbers. By using this result, we define an integral representation of twisted $l_{H,q}$-functions, which interpolates twisted $q$-generalized Frobenius-Euler numbers at negative integers. We also define twisted $q$-zeta functions. Furthermore, we give a relation between twisted $l_{H,q}$-functions and twisted $q$-zeta functions. We obtain new results related to the twisted $l_{H,q}$-function as well.

11S40Zeta functions and $L$-functions of local number fields
11S80Other analytic theory of local fields
11B68Bernoulli and Euler numbers and polynomials