p-Adic q-Twisted Dedekind-Type Sums

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Bayad A., ŞİMŞEK Y.

SYMMETRY-BASEL, vol.13, no.9, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 9
  • Publication Date: 2021
  • Doi Number: 10.3390/sym13091756
  • Journal Name: SYMMETRY-BASEL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: twisted (h, q)-Bernoulli polynomials, p-adic q-Dedekind sums, reciprocity law, Volkenborn integral, the Teichmuller character, RING, (H
  • Akdeniz University Affiliated: Yes

Abstract

The main purpose of this paper is to define p-adic and q-Dedekind type sums. Using the Volkenborn integral and the Teichmuller character representations of the Bernoulli polynomials, we give reciprocity law of these sums. These sums and their reciprocity law generalized some of the classical p-adic Dedekind sums and their reciprocity law. It is to be noted that the Dedekind reciprocity laws, is a fine study of the existing symmetry relations between the finite sums, considered in our study, and their symmetries through permutations of initial parameters.