报告题目：Zeta Functions and Character Sums
报告人：Jerome William Hoffman 教授
报告人单位：Louisiana State University, Baton Rouge
报告时间：2019年7月2日 ，上午10：00-11：00
报告地点：四牌楼逸夫建筑馆1502
报告摘要：
The talk will be elementary and accessible to undergraduates. I will explain the main idea of the zeta function Z(X/Fq,t) of a variety over a finite field. The zeta function is basically the counting function n 7! #X(Fqn), so this records the number of points of X in the finite fields Fqn. In particular, I will state the main structure of this, which is given by the Weil conjectures. In many instances, the zeta function can be explicitly computed in terms of character sums over finite fields. I will explain this for the Fermat curvexm+ym = zm, and related examples. Finally I will introduce some recent work where the character sums are closely related to hypergeometric functions.
报告人介绍：
Jerome William Hoffman, 美国路易斯安娜州立大学教授。1973年本科毕业于普林斯顿大学，1977年在Hironaka(Fields 1970)的指导下，在哈佛大学获得博士学位。长期从事代数几何与数论的研究，主要研究成果发表在Duke Math.J, Mem. Amer. Math. Soc, Advance.Math等多个有影响力的期刊上。