Fourth power mean values of one kind special Kloosterman's sum

Li Rui; Nilanjan Bag; Li Rui; Nilanjan Bag

doi:10.3934/era.2023326

Electronic Research Archive

2023, Volume 31, Issue 10: 6445-6453. doi: 10.3934/era.2023326

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Fourth power mean values of one kind special Kloosterman's sum

Li Rui ¹,
Nilanjan Bag ^{2
,
,}

1.
Department of Mathematics, Longnan Teachers College, Longnan, Gansu, China
2.
Department of Mathematics, Ramakrishna Mission Vivekananda Educational and Research Institute, Belur Math, Howrah, India

Received: 15 June 2023 Revised: 03 September 2023 Accepted: 15 September 2023 Published: 27 September 2023
11L03; 11L05

The main purpose of this article is using the analytic methods and properties of classical Gauss sums to study the calculating problem of fourth power mean values of one kind special Kloosterman's sum, and give a sharp asymptotic formula for it. At the same time, the paper also provides a new and effective method for the study of related power mean value problems.
- special Kloosterman's sums,
- fourth power mean,
- analytic method,
- asymptotic formula
Citation: Li Rui, Nilanjan Bag. Fourth power mean values of one kind special Kloosterman's sum[J]. Electronic Research Archive, 2023, 31(10): 6445-6453. doi: 10.3934/era.2023326

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Abstract

The main purpose of this article is using the analytic methods and properties of classical Gauss sums to study the calculating problem of fourth power mean values of one kind special Kloosterman's sum, and give a sharp asymptotic formula for it. At the same time, the paper also provides a new and effective method for the study of related power mean value problems.

References

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