报告题目: Zeros of Polynomials over Finite Fields报告人： Prof.  Xiang-dong Hou,  University of South Florida时间： 5月31日下午16：00-17：00

地点：五教5306摘要：

Let F_q be the finite field with q elements. For f in F_q[X_1,/dots,X_n], let Z(f) be the set of zeros of f in F_q^n. What can we say about |Z(f)|? This is a basic and central question in finite fields, number theory, and algebraic geometry. We survey various bounds for |Z(f)|; most of them are well known, but some are not well publicized. We will mention a series of theorems by Chevalley, Warning,Ax, and Katz,  the Delsarte-Goethals-MacWilliams Theorem on the minimum weight codewords of the Reed-Muller code, and the Hasse-Weil bound.