Multiple Dedekind Type Sums and Their Related Zeta Functions

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Bayad A., ŞİMŞEK Y.

MATHEMATICS, vol.9, no.15, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 15
  • Publication Date: 2021
  • Doi Number: 10.3390/math9151744
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: twisted (h, q)-Bernoulli numbers and polynomials, Barnes' type multiple zeta function, higher-order Bernoulli numbers and polynomials, Dedekind sums, reciprocity law, Q)-BERNOULLI NUMBERS, APOSTOL-BERNOULLI, TWISTED (H, POLYNOMIALS, PRODUCTS
  • Akdeniz University Affiliated: Yes

Abstract

The main purpose of this paper is to use the multiple twisted Bernoulli polynomials and their interpolation functions to construct multiple twisted Dedekind type sums. We investigate some properties of these sums. By use of the properties of multiple twisted zeta functions and the Bernoulli functions involving the Bernoulli polynomials, we derive reciprocity laws of these sums. Further developments and observations on these new Dedekind type sums are given.