Abstract
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.
Highlights
The Hecke operators have many applications in various spaces like the space of elliptic modular forms, the space of polynomials and others
The Hurwitz zeta functions and the Apostol-Bernoulli polynomials have been studied by many authors, for example, see
The main motivation of this paper is to introduce and study new Hecke-type operators on the ring of C[x]
Summary
The Hecke operators have many applications in various spaces like the space of elliptic modular forms, the space of polynomials and others. For more details on Hecke operators, see [ , ]. The Hurwitz zeta functions and the Apostol-Bernoulli polynomials have been studied by many authors, for example, see (cf [ – ], the others). We derive relations between these operators, the Hurwitz zeta functions and Apostol-Bernoulli type polynomials. There are many reasons for being interested by Hecke-type operators.
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