腾讯会议ID： 890161743
时间： 2023年3月21日 15：00- 17：00
报告人: 周海港 教授（同济大学）
题目: Siegel Eisenstein series of level two and its applications
时间: 3月21号 15：00-16：00
摘要: In this talk, we construct a holomorphic Siegel Eisenstein series of weight 2 and level 2, and compute its Fourier coefficients explicitly. Moreover, we prove that this modular form equals the generating function of the representative number ρ(n,m,r) associated with the maximal order in the quaternion algebra (-1,-1)Q. As applications, we give an explicit formula for the numbers of solutions of two systems of Diophantine equations related with Sun's “1-3-5 conjecture”.
个人简介: 同济大学数学科学学院教授, 博士生导师。主要从事数论与模形式研究，特别是在Jacobi形式理论方面。在《Trans. of AMS》和《Math Z.》等期刊发表多篇论文，主持多项国家自然科学基金项目，作为参与人获教育部2011年度高等学校科学研究优秀成果奖自然科学二等奖。
报告人：李英琨 教授(德国Technical University of Darmstadt)
时间 3月21号 16：00-17：00
题目: Algebraicity of higher Green functions at CM points.
摘要: By the classical theory of complex multiplication, the modular
j-function takes algebraic values at CM points. It is an interesting
question to ask about the algebraic nature of other types of automorphic
functions at CM points. For the automorphic Green function at integral
parameters, Gross and Zagier conjectured in the 1980s that their values at CM points are essentially logarithms of algebraic numbers. In this talk,
we will discuss recent progress toward this conjecture and its
generalization to the setting of orthogonal Shimura varieties. This is
partly joint with Jan Bruinier and Tonghai Yang.
个人简介：
李英琨, 2013年自UCLA获得数学博士学位，导师William Duke. 其后，在Cologne大学，波恩马普所和TU(technical university of Darmstadt)做博士后和访问教授。2018年始，在TU工作至今。研究领域是数论，特别是自守形式和算术研究。
