The fourth power mean of the three–term exponential sums

Xiaoge Liu , Guohui Chen

Electronic Research Archive ›› 2025, Vol. 33 ›› Issue (7) : 4329 -4342.

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Electronic Research Archive ›› 2025, Vol. 33 ›› Issue (7) :4329 -4342. DOI: 10.3934/era.2025197
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The fourth power mean of the three–term exponential sums
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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.

Keywords

three–term exponential sums / elementary methods / fourth power mean / identity

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Xiaoge Liu, Guohui Chen. The fourth power mean of the three–term exponential sums. Electronic Research Archive, 2025, 33 (7) : 4329-4342 DOI:10.3934/era.2025197

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