讲座题目：Pseudorandomness of Sato-Tate Distributions for Elliptic Curves
主讲人：莫仲鹏 教授
主持人：刘钢 教授
开始时间：2024-09-12 10:15
讲座地址：闵行校区数学楼102
主办单位：数学科学学院
报告人简介：
莫仲鹏教授，他的研究兴趣是：代数数论🧑🏻🦯➡️、自守表示论和朗兰兹纲领👨🏽🦰，在Mem. Amer. Math. Soc.、Compos. Math.🈴👨🏻⚕️、Comment. Math. Helv.、Math. Res. Lett.等著名数学刊物发表论文10余篇。代表荣誉👨🏿⚕️：加拿大安大略省，Early Researcher Award, 2012；美国李氏基金会👨🏼🔬，Li Foundation Heritage Prize, 2019🔌；2020年入选国家级人才计划青年学者项目。
报告内容：
Equidistribution is an important theme in number theory. The Sato-Tate conjecture, which was established by Richard Taylor et.al. in 2008, asserts that given an elliptic curve over Q without complex multiplication, the associated Frobenius angles are equidistributed with respect to the Sato-Tate measure. In this talk, we discuss refinements to the original Sato-Tate conjecture. In particular, we conjecture that the Frobenius angles are in fact statistically independently distributed with respect to the Sato-Tate measure, and satisfy a qualitative form of the Law of Iterated Logarithm for random numbers. Numerical evidence would be presented to support the conjectures. Joint work with Huimin Zheng.
