Hecke operators type and generalized Apostol-Bernoulli polynomials
Résumé
Abstract In this paper, we construct some Hecke-type operators acting on the complex polynomials space, and we prove their commutativity. By means of this commutativity, we find a new approach to establish the generating function of the Apostol-Bernoulli type polynomials which are eigenfunctions of these Hecke-type operators. Moreover, we derive many useful identities related to these operators and polynomials. MSC: 11M35, 30B40, 30B50.