On the generalized Cochrane sum with Dirichlet characters

Jiankang Wang; Zhefeng Xu; Minmin Jia; Jiankang Wang; Zhefeng Xu; Minmin Jia

doi:10.3934/math.20231542

AIMS Mathematics

2023, Volume 8, Issue 12: 30182-30193. doi: 10.3934/math.20231542

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Research article

On the generalized Cochrane sum with Dirichlet characters

Research Center for Number Theory and Its Applications, Northwest University, Xi'an 710127, China

Received: 01 September 2023 Revised: 06 October 2023 Accepted: 31 October 2023 Published: 07 November 2023
MSC : 11F20, 11L05

In this paper, we defined a new generalized Cochrane sum with Dirichlet characters, and gave the upper bound of the generalized Cochrane sum with Dirichlet characters. Moreover, we studied the asymptotic estimation problem of the mean value of the generalized Cochrane sum with Dirichlet characters and obtained a sharp asymptotic formula for it. By using this asymptotic formula, we also gave the mean value of the generalized Dedekind sum.
- generalized Cochrane sum,
- Dirichlet character,
- upper bound,
- mean value
Citation: Jiankang Wang, Zhefeng Xu, Minmin Jia. On the generalized Cochrane sum with Dirichlet characters[J]. AIMS Mathematics, 2023, 8(12): 30182-30193. doi: 10.3934/math.20231542

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Abstract

In this paper, we defined a new generalized Cochrane sum with Dirichlet characters, and gave the upper bound of the generalized Cochrane sum with Dirichlet characters. Moreover, we studied the asymptotic estimation problem of the mean value of the generalized Cochrane sum with Dirichlet characters and obtained a sharp asymptotic formula for it. By using this asymptotic formula, we also gave the mean value of the generalized Dedekind sum.

References

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