Quadratic Symmetric Polynomials and an analogue of the Davenport Constant

Abstract

In this paper, we define the constant $D(\phi ,p)$, an analogue for the Davenport constant, for sequences on the finite field ${\mathbb{F}}_p$, defined via quadratic symmetric polynomials. Next, we state a series of results presenting either the exact value of $D(\phi ,p)$, or lower and upper bounds for this constant.