The main result of this paper is a coefficient formula that sharpens and generalizes Alon and
Tarsi's Combinatorial Nullstellensatz. On its own, it is a result about polynomials, providing …

Let F q be a finite field of characteristic p and order q. The Chevalley–Warning Theorem
asserts that the set V of common zeros of a collection of polynomials must satisfy| V|≡ 0 mod …

This paper presents a study of perturbations of symmetric Boolean functions. In particular, it
establishes a connection between exponential sums of these perturbations and Diophantine …

We define the p-density of a finite subset D⊂ Nr, and show that it gives a sharp lower bound
for the p-adic valuations of the reciprocal roots and poles of zeta functions and L-functions …

This work brings techniques from the theory of recurrent integer sequences to the problem of
balancedness of symmetric Boolean functions. In particular, the periodicity modulo p (p odd …

We determine the greatest common divisor of the cardinalities of the algebraic sets
generated by collections of polynomials $ f_1,\ldots, f_t $ of specified degrees $ d_1,\ldots …

In this paper we compute the exact 2-divisibility of exponential sums associated to
elementary symmetric Boolean functions. Our computation gives an affirmative answer to …

Let F q denote the finite field of q elements with characteristic p. Let Z q denote the
unramified extension of the p-adic integers Z p with residue field F q. In this paper, we …

Kloosterman sums are exponential sums on finite fields that have important applications in
cryptography and coding theory. We use Stickelberger's theorem and the Gross-Koblitz …

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 …