When Pólya-Vinogradov meets van der Corput
数学公众报告（120 周年校庆系列第3场）
报告题目(Title)：When Pólya-Vinogradov meets van der Corput
报告人(Speaker)：郗平教授 （西安交通大学）
地点(Place)：腾讯会议ID: 932 113 954 密码：123456
时间(Time)：2021 年 12 月 3 日（周五） 15:00--16:30
邀请人(Inviter)：蒲飞
报告摘要
Exponential sums of analytic and algebraic types are both fundamental and have found many important applications in number theory and allied areas. The celebrated Pólya-Vinogradov method is able to produce non-trivial estimates as long as the interval is a bit longer than the squareroot of the modulus, this, however, is no longer valid if the interval becomes much shorter. In this talk, we will explain how to introduce the classical ideas of van der Corput on analytic exponential sums, following Heath-Brown, to algebraic settings so that one can beat the Pólya-Vinogradov barrier as long as the modulus has small prime factors. More importantly, we are able to develop the method of arithmetic exponent pairs for general algebraic trace functions (jointly with Jie Wu from CNRS). Several applications to number theory will also be mentioned in the end.
主讲人简介
郗平，西安交通大学教授，博士生导师，国家杰出青年基金获得者。主要研究领域为数论，涉及代数迹函数的解析理论、素数分布、筛法及自守形式等方面的研究。研究成果发表于Inventiones mathematicae、Compositio Mathematica、Algebra & Number Theory、International Mathematics Research Notices等国际数学期刊。
