讲座题目：Exponential sums on curves over finite fields: the large genus asymptotc theory
主讲人：莫仲鹏 教授
主持人：谢兵永 教授
开始时间：2025-09-25 11:00
讲座地址：闵行校区数统楼北楼102报告厅
主办单位：数学科学学院
报告人简介：
莫仲鹏，上海数学与交叉学科研究院教授，毕业于哈佛大学，师从著名数学家Mazur, 研究领域为代数数论，主要涉及Langlands纲领，也涉及有限域相关问题。
报告内容：
We initiate the study of asymptotic properties of exponential sums on smooth projective curves over finite fields, as the genus tends to infinity (with the finite field being fixed). Specifically, as an analogue of the original Ihara constant, we introduce a version of the Ihara constant for exponential sums, and prove that it satisfies the analogue of the Drinfeld-Vladut upper bound, and also the lower bound of Bassa-Beelen-Garcia-Stichtenoth obtained for the original Ihara constant, when the cardinality of the finite field is not a prime. In particular it reaches the optimal Drinfeld-Vladut bound when the cardinality of the finite field is a square. In addition, we use results on infinite class field towers to show that the exponential sum version of the Ihara constant is positive in general. Finally by using the analytic technique of explicit formula, we also obtain an analogue of Tsfasman’s basic inequality for these exponential sums. Joint work with Xiaoyu Wang.
