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http://dx.doi.org/10.4134/JKMS.2006.43.1.111

p-ADIC q-HIGHER-ORDER HARDY-TYPE SUMS  

SIMSEK YILMAZ (Akdeniz University Faculty of Art and Science Department of Mathematics)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.1, 2006 , pp. 111-131 More about this Journal
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 padic q-analogue of higher-order Hardy-type sums. By using an invariant p-adic q-integral on $\mathbb{Z}_p$, we give fundamental properties of these sums. We also establish relations between p-adic Hardy sums, Bernoulli functions, trigonometric functions and Lambert series.
Keywords
Dedekind sums; p-adic Dedekind sums; generalized Dedeking sums; Hardy sums; Bernoulli polynomizls and functions; Lambert series p-adic q-higher order Dedekind sums; p-adic q-Bernoulli numbers;
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