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Research Article | Open Access

On quadratic character sums of multivariate symmetric polynomials modulo p

Shaofan Cao1( ), Tingting Wang2
School of Science, China University of Mining and Technology, Beijing 100083, China
College of Science, Northwest A&F University, Yangling 712100, China
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Abstract

In this paper, we use the elementary and analytic methods to investigate the computational problem of quadratic character sums related to quaternary and quintuple symmetric polynomials modulo a prime p, respectively. By applying properties of Gauss sums and those of third-order characters modulo p, we establish some identities for such quadratic character sums in the cases of ( 3 , p − 1 ) = 1 and ( 3 , p − 1 ) = 3.

Keywords

quadratic character sumsclassical Gauss sumsmultivariate symmetric polynomialsthird-order characters

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Electronic Research Archive
Volume 33 Issue 12,
December 2025
Pages 7491-7508
DOI: 10.3934/era.2025330

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Cao S, Wang T. On quadratic character sums of multivariate symmetric polynomials modulo p. Electronic Research Archive, 2025, 33(12): 7491-7508. https://doi.org/10.3934/era.2025330

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Received: 14 October 2025
Revised: 30 November 2025
Accepted: 09 December 2025
Published: 11 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)