Pseudorandomness of Sato-Tate Distributions for Elliptic Curves
Prof. Chung Pang Mok
2023-04-12 10:30-11:30
MCM110&Online
Speaker: Prof. Chung Pang Mok (Soochow University)Time: 10:30-11:30 April 12, 2023 (Wednesday)
Place: MCM 110 & Online (Zoom ID: 4663562952 Password: mcm1234)
Title: Pseudorandomness of Sato-Tate Distributions for Elliptic Curves
Abstract: 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 evidences would be presented to support the conjectures. Joint work with Huimin Zheng.
