• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.611-622
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• 2023

The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that q is a prime.

• 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.