Hecke operators type and generalized Apostol-Bernoulli polynomials


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Aygüneş A. A., Bayad A., ŞİMŞEK Y.

FIXED POINT THEORY AND APPLICATIONS, vol.2013, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1186/1687-1812-2013-92
  • Journal Name: FIXED POINT THEORY AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Hecke operators, Hurwitz zeta function, generalized Apostol-Bernoulli type polynomials, Bernoulli polynomials, Euler polynomials, EULER
  • Akdeniz University Affiliated: Yes

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.