Article ID Journal Published Year Pages File Type
4595549 Journal of Number Theory 2007 7 Pages PDF
Abstract

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, such as Chavelley, Warning, Ax, Katz, etc. In this paper, by reducing the degree of a given polynomial meanwhile remaining the number of its zeros unchanged, we present an improvement upon the Chevalley–Warning–Ax–Katz-type estimates in many cases. Furthermore, our result can improve Cao–Sun's reduction recently obtained on counting the number of zeros of general diagonal equations over finite fields.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory