Arithmetic of modular forms and Shimura Curves
Dr. Jia-Wei Guo
(Department of Mathematics, National Taiwan University)
As highly symmetric objects, modular forms encode an extraordinary amount of deep arithmetic and geometric information. In this talk, we will discuss some basic properties of modular forms and Shimura curves and their relations with arithmetic and geometry. As an example, we will present coefficients of Cohen’s Eisenstein series of weight 5/2 as some new class number relations. These relations arise from the intersections of Shimura curves and Humbert surfaces on the Siegel modular threefold, and can be considered as a higher-dimensional analogue of the classical Hurwitz-Kronecker class number relation.
日 期：108年12月4日(星期三) 16:10~17:00