Hybrid mean values of Dedekind sums via Williams' transformation formula and applications to Kloosterman sums

Wenpeng Zhang; Li Wang; Wenpeng Zhang; Li Wang

doi:10.3934/era.2026377

Electronic Research Archive

2026, Volume 34, Issue 12: 8977-8986. doi: 10.3934/era.2026377

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Research article

Hybrid mean values of Dedekind sums via Williams' transformation formula and applications to Kloosterman sums

Wenpeng Zhang ¹,
Li Wang ^{2
,
,}

1.
Institute of Mathematics, Aba Teachers College, Aba, China
2.
School of Electronic Information, Northwest University, Xi'an, China

Received: 08 May 2026 Revised: 23 September 2026 Accepted: 15 October 2026 Published: 23 October 2026

By combining analytic number theory methods with Williams's classical work, this paper investigated the computational problem of a class of power means involving Dedekind sums, and established a novel explicit conversion identity. Furthermore, we obtained exact formulas for even power means of Kloosterman sums via properties of character sums.
- Dedekind sums,
- Kloosterman sums,
- Williams' transformation formula,
- asymptotic formula
Citation: Wenpeng Zhang, Li Wang. Hybrid mean values of Dedekind sums via Williams' transformation formula and applications to Kloosterman sums[J]. Electronic Research Archive, 2026, 34(12): 8977-8986. doi: 10.3934/era.2026377

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Abstract

By combining analytic number theory methods with Williams's classical work, this paper investigated the computational problem of a class of power means involving Dedekind sums, and established a novel explicit conversion identity. Furthermore, we obtained exact formulas for even power means of Kloosterman sums via properties of character sums.

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