On quadratic character sums of multivariate symmetric polynomials modulo p

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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 sums / classical Gauss sums / multivariate symmetric polynomials / third-order characters

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