An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem

分析学研讨班

题目：An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem

报告人：杨学睿（伊利诺伊大学厄巴纳-香槟分校）

时间：12月20日（星期三），14:30-16:00

地点：明德楼B201-1

Zoom会议，会议号：995 9561 4888，密码：461559

摘要：Using Bombieri-Iwaniec method, we establish an improvement on both Gauss's Circle Problem and Dirichlet's Divisor Problem. More precisely, we derive a new estimate for the first spacing problem and combine it with Huxley's results on the second spacing problem. In this talk, I will talk about several methods to deal with exponential sums on the integer ring, with focus on the Bombieri-Iwaniec method. After that, I will talk about several results in decoupling theory as well as some rough ideas in the proofs.

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