On the high-th mean of one special character sums modulo a prime

Yan Ma; Di Han; Yan Ma; Di Han

doi:10.3934/math.20231316

AIMS Mathematics

2023, Volume 8, Issue 11: 25804-25814. doi: 10.3934/math.20231316

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Research article

On the high-th mean of one special character sums modulo a prime

Yan Ma ,
Di Han ^,

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

Received: 28 June 2023 Revised: 11 August 2023 Accepted: 17 August 2023 Published: 07 September 2023
MSC : 11L05, 11L40

Using the elementary method of the classical Gauss sums and the properties of character sums, we study a linear recurrence formula about the form $ G\left(n\right) = 1+\sum_{a = 1}^{p-1}\left(\frac{a^2+n\bar{a}^2}{p}\right) $ and about the mean value of $ G(n) $. This is a further exploration of Yuan and Zhang's research in 2022, which help us to better understand the character sums wide range application.
- quadratic character,
- quartic character,
- basic method,
- calculating formula,
- special character sums
Citation: Yan Ma, Di Han. On the high-th mean of one special character sums modulo a prime[J]. AIMS Mathematics, 2023, 8(11): 25804-25814. doi: 10.3934/math.20231316

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Abstract

Using the elementary method of the classical Gauss sums and the properties of character sums, we study a linear recurrence formula about the form $ G\left(n\right) = 1+\sum_{a = 1}^{p-1}\left(\frac{a^2+n\bar{a}^2}{p}\right) $ and about the mean value of $ G(n) $. This is a further exploration of Yuan and Zhang's research in 2022, which help us to better understand the character sums wide range application.

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