報告題目：Equidistribution of quadratic roots and applications to prime number theory
報告人：郗平（西安交通大學）
報告時間：2020年12月18日（星期五）15:30開始
報告地點：騰訊會議線上報告
會議ID：117 970 483
報告摘要：Given an irreducible quadratic polynomial of fixed discriminant, the quadratic roots mod m are expected to be equidistributed as m runs over reasonable sets. We will give a short historical survey on this topic, as well as our recent progress on the case of friable moduli (based on the joint with Cécile Dartyge and Jie Wu). Moreover, a reasonable equidistribution can also lead to non-trivial multiplicative structures in prime number theory, and an application to a special case of Schinzel hypothesis will be discussed in this talk. The underlying tools will include Gauss’s correspondence in the theory of binary quadratic forms and arithmetic exponent pairs for trace functions developed by Jie Wu and the speaker.
報告人簡介：郗平，西安交通大學教授、博士生導師，主要研究領域為數論，涉及代數跡函數的解析理論、素數分布、篩法及自守形式等方面的研究。研究成果發表于Inventiones mathematicae、Compositio Mathematica、International Mathematics Research Notices、Mathematische Zeitschrift等國際數學期刊。目前主持國家杰出青年科學基金、國家自然科學基金面上項目及中法合作交流項目各一項。