Effective joint equidistribution of primitive rational points on expanding horospheres

Abstract

In this talk, we will discuss effective joint equidistribution of primitive rational points on expanding horospheres in the space of unimodular lattices in any dimension. (For 1-dimentional case, this is joint equidistribtion of {a/q,b/q} where ab=1 mod q, as q goes to infinity.) The proof uses Fourier analysis and Weil’s bounds of Kloosterman sums. As an application, we provide a rate of convergence to the limiting distribution for the diameters of random circulant graphs. This is joint work with Daniel El-Baz and Min Lee.

Speaker

黄炳荣，山东大学数据科学研究院教授、博导，山东大学杰出中青年学者，入选国家级青年人才计划、山东省泰山学者青年专家。所在中心为大数据理论研究中心，研究方向为数论。主要研究兴趣是解析数论、自守形式和 L-函数的解析理论、算术量子混沌等。

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https://faculty.sdu.edu.cn/brhuang/zh_CN/index.htm