Module form lecture notes

Author: Lu Hongwen Li Yunfeng (editors)
Publisher:
Publish Date: 2001-04-01
Features: Modular forms are analytic functions that possess certain invariance properties under a certain group of transformations. Their emergence and development from the mid-19th century to the present reflect the evolution of classical number theory into modern number theory, especially playing an irreplaceable role in the recent proof of Fermat's Last Theorem by A. Wiles. Moreover, they have demonstrated increasingly promising prospects in other branches of mathematics and practical applications. The book is divided into three parts, comprising 14 chapters. Part I discusses modular forms of SL?(Z); Part II covers general integer-weight modular forms; and Part III addresses half-integer-weight modular forms. The book systematically elaborates on topics such as symplectic geometry, base fields, dimension formulas, Hecke theory, Weil's theorem, trace formulas, and half-integer-weight modular forms. Part I of the book can serve as a textbook for senior undergraduate students and master's degree candidates in relevant fields of mathematics, while Part II and Part III are suitable for doctoral students in related disciplines. The entire book can also serve as a reference for mathematicians in the field.