丘成桐中心代数与数论组周五讨论班
SEU Yau Center Algebra and Number Theory Weekly Seminar
为活跃中心学术氛围，促进成员间的学术交流并激发合作，丘成桐中心代数与数论组将从2022年10月末开始定期组织周五讨论班。周五讨论将面向代数与数论组、全体中心成员、数学学院研究生及感兴趣的校内外师生。
2022年11月11日，代数与数论组周五讨论班将由曹炜教授主讲，报告信息如下。
Title: L-Functions of Twisted Exponential Sums
Speaker: Prof. WeiCAO (曹炜)
Affiliation: Minnan Normal University（闽南师范大学)
Time: 14:00-15:00, Friday, November 11th, 2022 (UTC+8, Beijing Time)
Venue: 腾讯会议/VooV Meeting (697-851-613)
入会链接: https://meeting.tencent.com/dm/nSS6mVtXsvbb
Abstract
Let F_q be the finite field of q elements and χ_1,...,χ_n be the multiplicative characters of F_q. For a given Laurent polynomial f in n variables over F_q, the corresponding L-function is defined to be L(χ_1,...,χ_n,f;T)=exp(ΣS_h(χ_1,...,χ_n,f)T^h/h), where the sum runs over all positive integers h and S_h(χ_1,...,χ_n,f) is the twisted exponential sum defined in the extension of F_q of degree h. In this talk, I will give the explicit formula for L(χ_1,...,χ_n,f;T) of the Laurent polynomial with full column rank degree matrix in terms of p-adic gamma functions, which generalizes the results of Wan, Hong and Cao. As applications, we will evaluate the slopes of the reciprocal zeros and reciprocal poles of L(χ_1,...,χ_n,f;T), determine the p-adic Newton polygons of the polynomials associated to the L-function L(χ_1,...,χ_n,f;T), and compute the zeta functions of certain algebraic varieties over finite fields. This is a joint work with Professor Shaofang Hong.
About the Speaker
曹炜，闽南师范大学教授，博士生导师，福建省“闽江学者”特聘教授。1992年-1997年在北京大学概率统计系本科学习，2002年-2007年在四川大学数学学院硕博连读，获理学博士学位。主要研究兴趣为：数论、有限域及其应用。已发表学术论文60余篇，主持或完成中国博士后科学基金、国家自然科学基金、福建省自然科学基金、宁波市自然科学基金等多项科研项目。