Generalized polynomial exponential sums and their fourth power mean

Li Wang; Yuanyuan Meng; Li Wang; Yuanyuan Meng

doi:10.3934/era.2023220

Electronic Research Archive

2023, Volume 31, Issue 7: 4313-4323. doi: 10.3934/era.2023220

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Generalized polynomial exponential sums and their fourth power mean

Li Wang ,
Yuanyuan Meng ^,

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

Received: 22 December 2022 Revised: 15 May 2023 Accepted: 25 May 2023 Published: 05 June 2023

The study of the power mean of the generalized polynomial exponential sums plays a very important role in analytic number theory, and many classical number theory problems are closely related to it. In this article, we use the elementary methods and the properties of the exponential sums to study the calculating problem of one kind of fourth power mean of some special generalized polynomial exponential sums, and we give some exact calculating formulae for them.
- generalized polynomial exponential sums,
- fourth power mean,
- elementary method,
- exact calculating formula
Citation: Li Wang, Yuanyuan Meng. Generalized polynomial exponential sums and their fourth power mean[J]. Electronic Research Archive, 2023, 31(7): 4313-4323. doi: 10.3934/era.2023220

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Abstract

The study of the power mean of the generalized polynomial exponential sums plays a very important role in analytic number theory, and many classical number theory problems are closely related to it. In this article, we use the elementary methods and the properties of the exponential sums to study the calculating problem of one kind of fourth power mean of some special generalized polynomial exponential sums, and we give some exact calculating formulae for them.

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