@article{Cao2025, 
author = {Shaofan Cao and Tingting Wang},
title = {On quadratic character sums of multivariate symmetric polynomials modulo    p},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {12},
pages = {7491-7508},
keywords = {quadratic character sums, classical Gauss sums, multivariate symmetric polynomials, third-order characters},
url = {https://www.sciopen.com/article/10.3934/era.2025330},
doi = {10.3934/era.2025330},
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.}
}