科学研究
报告题目:

Burgess’ method and applications

报告人:

郗平 教授(西安交通大学)

报告时间:

报告地点:

腾讯会议 ID:737 894 769

报告摘要:

Starting from 1950’s, D. A. Burgess has developed an ingenious approach to estimate incomplete character sums, appealing to Weil’s proof on Riemann Hypothesis for curves over finite fields. This allows him to break the barrier of Pólya-Vinogradov and thus works nontrivially for suitably short character sums. Burgess’ method has been simplified and generalized in the subsequent decades thanks to Karatsuba, Friedlander--Iwaniec, Fouvry--Michel, et al, and it turns out to be very powerful in many applications of Fourier analysis to number theory. In this talk, I will give a brief introduction to the relevant history, and present our recent work on estimates for bilinear forms of trace functions over finite fields with the aid of additive combinatorics.

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