대한수학회지 (Journal of the Korean Mathematical Society)

  • 제43권1호
  • /
  • Pages.111-131
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  • 2006
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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p-ADIC q-HIGHER-ORDER HARDY-TYPE SUMS

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

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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참고문헌

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피인용 문헌

  1. q-Hardy–Berndt type sums associated with q-Genocchi type zeta and q-l-functions vol.71, pp.12, 2009, https://doi.org/10.1016/j.na.2008.11.014
  2. Special functions related to Dedekind-type DC-sums and their applications vol.17, pp.4, 2010, https://doi.org/10.1134/S1061920810040114
  3. Transformation formulas of a character analogue of $$\log \theta _{2}(z)$$logθ2(z) pp.1572-9303, 2018, https://doi.org/10.1007/s11139-018-0042-7