Exact 𝑝-divisibility of exponential sums via the covering method

Castro, Francis; Rubio, Ivelisse

doi:10.1090/S0002-9939-2014-12315-X

Exact $p$-divisibility of exponential sums via the covering method
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by Francis Castro and Ivelisse M. Rubio PDF

Proc. Amer. Math. Soc. 143 (2015), 1043-1056 Request permission

Abstract:

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.

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