The sixth power mean of one kind generalized two-term exponential sums and their asymptotic properties

Jin Zhang; Xiaoxue Li; Jin Zhang; Xiaoxue Li

doi:10.3934/era.2023234

Electronic Research Archive

2023, Volume 31, Issue 8: 4579-4591. doi: 10.3934/era.2023234

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The sixth power mean of one kind generalized two-term exponential sums and their asymptotic properties

Jin Zhang ¹,
Xiaoxue Li ^{2
,
,}

1.
School of Information Engineering, Xi'an University, Xi'an, Shaanxi, China
2.
School of Science, Xi'an Aeronautical Institute, Xi'an, Shaanxi, China

Received: 19 January 2023 Revised: 13 June 2023 Accepted: 15 June 2023 Published: 26 June 2023

The main aim of this article is using the elementary method and the number of the solutions of some congruence equations modulo an odd prime $ p $, to study the calculating problem of the sixth power mean of one kind generalized two-term exponential sums, and give a sharp asymptotic formula for it.
- the generalized two-term exponential sums,
- sixth power mean,
- elementary method,
- asymptotic formula
Citation: Jin Zhang, Xiaoxue Li. The sixth power mean of one kind generalized two-term exponential sums and their asymptotic properties[J]. Electronic Research Archive, 2023, 31(8): 4579-4591. doi: 10.3934/era.2023234

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Abstract

The main aim of this article is using the elementary method and the number of the solutions of some congruence equations modulo an odd prime $ p $, to study the calculating problem of the sixth power mean of one kind generalized two-term exponential sums, and give a sharp asymptotic formula for it.

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