p-adic q-higher-order Hardy-type sums

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Simsek Y.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, vol.43, no.1, pp.111-131, 2006 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 43 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.4134/jkms.2006.43.1.111
  • Journal Name: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.111-131
  • Keywords: Dedekind sums, p-adic Dedekind sums, generalized Dedekind sums, Hardy sums, Bernoulli polynomials and functions, Lambert series p-adic q-higher order Dedekind sums, p-adic q-Bernoulli numbers, DEDEKIND SUMS, ZETA-FUNCTIONS, INTEGRALS
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

The goal of this paper is to define p-adic Hardy sums and p-adic q-higher-order Hardy-type sums. By using these sums and p-adic q-higher-order Dedekind sums, we construct p-adic continuous functions for an odd prime. These functions contain p-adic q-analogue of higher-order Hardy-type sums. By using an invariant p-adic q-integral on Z(p), we give fundamental properties of these sums. We also establish relations between p-adic Hardy sums, Bernoulli functions, trigonometric functions and Lambert series.