一、讲座主题

Introduction to exponential sums and an application to digits I-III

二、时间

9月20日（周五）09:30-11:00

9月23日（周一）15:00-16:30

9月27日（周五）09:30-11:00

三、地点

中心校区知新楼B座1044报告厅

四、主讲人

Thomas STOLL

五、主讲人简介

Thomas STOLL is currently a Professor of Mathematics at the Institute Elie Cartan at Nancy (University of Lorraine, France). He did his PhD in Graz (Austria) in 2004 under the supervision of R. Tichy and was rewarded with a research grant from the Austrian Academy of Sciences for a postdoc in Waterloo (Canada). He got a tenured position (Associate Professor) at Aix-Marseille University in Marseille (France) in 2009, and holds the position of a Full Professor in Nancy since 2012. His main areas of interest are analytic and combinatorial number theory with topics such as exponential sums, digital expansions, orthogonal polynomials and Diophantine equations. He has 36 publications.

六、摘要

This mini-course is a (gentle) introduction to exponential sums with the aim to give an application to a problem concerning digits of integers. In the first few lectures, we will develop the classical theory, such as Weyl's differencing method, Weyl's criterion and uniform distribution mod 1, discrepancy and the Erdoes-Turan inequality, as well as van der Corput's method. The last lecture is a scientific talk: I will show how these classical tools can be used to show that the sum of digits in base 2 and 3 can be "very often very close". This last part is recent joint research with R. de la Bretèche and G. Tenenbaum. No prerequisites are needed to follow the mini-course and the scientific talk.

七、邀请人

刘建亚 数学学院教授

八、主办

山东大学数学学院