JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, vol.43, no.1, pp.111-131, 2006 (SCI-Expanded)
Article / Article
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
Science Citation Index Expanded (SCI-EXPANDED), Scopus
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
Akdeniz University Affiliated:
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.