On the sixth power mean of one kind two-term exponential sums weighted by Legendre's symbol modulo $ p $

Wenpeng Zhang; Yuanyuan Meng; Wenpeng Zhang; Yuanyuan Meng

doi:10.3934/math.2021408

AIMS Mathematics

2021, Volume 6, Issue 7: 6961-6974. doi: 10.3934/math.2021408

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On the sixth power mean of one kind two-term exponential sums weighted by Legendre's symbol modulo $ p $

Wenpeng Zhang ,
Yuanyuan Meng ^,

School of Mathematics, Northwest University, Xi'an 710127, China

Received: 03 February 2021 Accepted: 19 April 2021 Published: 25 April 2021
MSC : 11L03, 11L05

The main purpose of this article is using the elementary methods and the properties of the character sums of the polynomials to study the calculating problem of one kind sixth power mean of the two-term exponential sums weighted by Legendre's symbol modulo $ p $, an odd prime, and give an interesting calculating formula for it.
- the two-term exponential sums,
- the sixth power mean,
- elementary method,
- calculating formula
Citation: Wenpeng Zhang, Yuanyuan Meng. On the sixth power mean of one kind two-term exponential sums weighted by Legendre's symbol modulo $ p $[J]. AIMS Mathematics, 2021, 6(7): 6961-6974. doi: 10.3934/math.2021408

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Abstract

The main purpose of this article is using the elementary methods and the properties of the character sums of the polynomials to study the calculating problem of one kind sixth power mean of the two-term exponential sums weighted by Legendre's symbol modulo $ p $, an odd prime, and give an interesting calculating formula for it.

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