A new generalization of Hardy-Berndt sums

DAĞLI M. C., CAN M.

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, vol.123, no.2, pp.177-192, 2013 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 123 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.1007/s12044-013-0125-8
  • Journal Name: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.177-192
  • Keywords: Dedekind sums, Hardy-Berndt sums, Bernoulli numbers and polynomials, DEDEKIND SUMS, THETA-FUNCTIONS, DEGENERATE, EISENSTEIN, NUMBERS, SERIES
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, we construct a new generalization of Hardy-Berndt sums which are explicit extensions of Hardy-Berndt sums. We express these sums in terms of Dedekind sums S-r (h, k : x, y/lambda) with x = y = 0 and obtain corresponding reciprocity formulas.