Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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p-ADIC q-HIGHER-ORDER HARDY-TYPE SUMS

  • SIMSEK YILMAZ (Akdeniz University Faculty of Art and Science Department of Mathematics)
  • Published : 2006.01.01
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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.

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