On the $ k $-th power mean of one kind generalized cubic Gauss sums

Xiaoge Liu; Yuanyuan Meng; Xiaoge Liu; Yuanyuan Meng

doi:10.3934/math.20231093

AIMS Mathematics

2023, Volume 8, Issue 9: 21463-21471. doi: 10.3934/math.20231093

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Research article

On the $ k $-th power mean of one kind generalized cubic Gauss sums

Xiaoge Liu ,
Yuanyuan Meng ^,

Research Center for Number Theory and Its Applications, Northwest University, Xi'an, 710127, Shaanxi, China

Received: 21 February 2023 Revised: 26 June 2023 Accepted: 28 June 2023 Published: 05 July 2023
MSC : 11L03, 11L05

The main purpose of this paper is using the elementary methods and properties of the recurrence sequence to study the calculating problem of the $ k $-th power mean of one kind generalized cubic Gauss sums, and give an exact calculating formula for it.
- the generalized Gauss sums,
- $ k $-th power mean,
- elementary method,
- recurrence sequence,
- calculating formula
Citation: Xiaoge Liu, Yuanyuan Meng. On the $ k $-th power mean of one kind generalized cubic Gauss sums[J]. AIMS Mathematics, 2023, 8(9): 21463-21471. doi: 10.3934/math.20231093

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Abstract

The main purpose of this paper is using the elementary methods and properties of the recurrence sequence to study the calculating problem of the $ k $-th power mean of one kind generalized cubic Gauss sums, and give an exact calculating formula for it.

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