The fourth power mean of the three–term exponential sums

Xiaoge Liu; Guohui Chen; Xiaoge Liu; Guohui Chen

doi:10.3934/era.2025197

Electronic Research Archive

2025, Volume 33, Issue 7: 4329-4342. doi: 10.3934/era.2025197

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Research article

The fourth power mean of the three–term exponential sums

Xiaoge Liu ^{1
,
,},
Guohui Chen ²

1.
Research Center for Number Theory and its Applications, School of Mathematics, Northwest University, Xi'an, China
2.
College of Mathematics and Statistics, Hainan Normal University, Hainan, China

Received: 27 November 2024 Revised: 25 February 2025 Accepted: 01 May 2025 Published: 29 July 2025

By employing trigonometric sums and solving congruence equations, this paper explores the power mean of a specific class of high–order three–term exponential sums, and derives intriguing identities in the process. The findings presented in this paper offer insights into establishing the lower bound for these sums.
- three–term exponential sums,
- elementary methods,
- fourth power mean,
- identity
Citation: Xiaoge Liu, Guohui Chen. The fourth power mean of the three–term exponential sums[J]. Electronic Research Archive, 2025, 33(7): 4329-4342. doi: 10.3934/era.2025197

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Abstract

By employing trigonometric sums and solving congruence equations, this paper explores the power mean of a specific class of high–order three–term exponential sums, and derives intriguing identities in the process. The findings presented in this paper offer insights into establishing the lower bound for these sums.

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