• Title/Summary/Keyword: Lambert series p-adic q-higher order Dedekind sums

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

  • SIMSEK YILMAZ
    • Journal of the Korean Mathematical Society
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    • v.43 no.1
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    • pp.111-131
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    • 2006
  • 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.