The course will be an introduction to the theory of modular forms. Modular forms are very special holomorphic functions on the upper half plane and play an important role in various fields of mathematics. In this course, we will define modular forms on the upper half plane, study the modular curves as Riemann surfaces defined by congruence subgroups, explore the structure of the spaces of modular forms, define Hecke operators, Petersson products and study the theory of old forms and newforms. Then we will define L-functions for eigenforms and study the Rankin-Selberg method for a pair of modular forms. The course is designed for students with background in basic complex analysis and familiar with basic notions of algebra and aims to open the door for deeper topics in modern number theory and arithmetic geometry.
- begleitende Lehrperson: Gautier Jean Christian Ponsinet
- verantwortliche Lehrperson: Xiaoyu Zhang