Given a system of polynomial equations over a finite field, estimating the p-divisibility of the
number of solutions of the system is a classical problem which has been studied extensively …

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 …

In this work, we introduce the p-weight degree of a polynomial over a finite field with respect
to a subset of the variables. Using this p-weight, we improve the results of Moreno and …

We give conditions under which the number of solutions of a system of polynomial equations
over a finite field $\mathbb {F} _q $ of characteristic $ p $ is divisible by $ p $. Our setup …

We prove that, under some natural conditions, given a system of polynomials F1,···, Ft with
monomials of disjoint support, any system F1+ G1,···, Ft+ Gt, where the p-weight degree of …

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 …

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 …

Let f be a polynomial over finite field Fq with q elements and let N (f= 0) denote the number
of zeros of f in Fq. The q-divisibility properties of N (f= 0) have been studied by many authors …

We present an elementary method to compute the exact p-divisibility of exponential sums of
systems of polynomial equations over the prime field. Our results extend results by Carlitz …

Schinzel's Hypothesis H predicts that a family of irreducible polynomials over the integers
satisfying certain necessary local conditions simultaneously assumes prime values infinitely …