一、题目：

A conjecture of Sárközy on quadratic residues

二、主讲人：

郗平

三、摘要：

A basic question in additive number theory is to study the sumset for suitably arbitrary sets with some prescribed structures. A conjecture of András Sárközy asserts, for all sufficiently large primes , that no sumset with consists of all quadratic residues mod exactly. Sárközy himself proved the ternary analogue of this conjecture, and the original one seems beyond the current techniques. In this talk, we discuss some tight bounds for the possible binary decompositions, which are based on Weil’s bound for complete character sums over finite fields, improving some previous works by I. E. Shparlinski, I. D. Shkredov, and Y.-G. Chen and X.-H. Yan.

This is joint work with Yong-Gao Chen.

四、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。

五、邀请人：

黄炳荣

六：时间：

3月2日（周三）21:00-22:00

七、地点：

腾讯会议，会议ID：358-9878-8585

八：主办方：

山东大学数学学院