Modal form guidance

Author: Pan Chengdong
Publisher:
Publish Date: 2002-06-01
Features: Modular form theory plays a very important role in the proof of Fermat's Last Theorem by A. Wiles, making it one of the mathematical branches that are currently of great interest and desire to learn about among the mathematical community and young students. This book serves as an introductory textbook for the "Modular Forms" course for senior undergraduate students and beginning graduate students (not necessarily specializing in number theory) in mathematics departments of comprehensive universities. The book is divided into twelve chapters. The content includes: elliptic functions, Eisenstein series G2k(T) for the full modular group, the full modular group, congruence subgroups of the full modular group, basic knowledge of modular functions, modular forms for congruence subgroups, Poincaré series, Hecke operators on the space of modular forms for the full modular group, Hecke operators on the space of modular forms for congruence subgroups, modular forms and Dirichlet series, two applications of modular forms, and related appendices. Chapters and the appendix of the twelfth chapter are the foundational knowledge of the entire book, laying the groundwork for the content discussed in each chapter. This book can be used as a textbook for senior undergraduate and graduate students in mathematics departments of comprehensive universities and normal universities, as well as for young teachers, mathematicians, and number theory enthusiasts.