Exact $p$-divisibility of exponential sums via the covering method
Francis N. Castro, Ivelisse M. Rubio · Proceedings of the American Mathematical Society · 2014
In general, the methods to estimate the $p$-divisibility of exponential sums or the number of solutions of systems of polynomial equations over finite fields are non-elementary. In this paper we present the covering method, an elementary combinatorial method that can be used to compute the exact $p$-divisibility of exponential sums over a prime field. The results here allow us to compute the exact $p$-divisibility of exponential sums of new families of polynomials, to unify and improve previously known results, and to construct families of systems of polynomial equations over finite fields that are solvable.