Module form and trace formula

Author: Ye Yangbo
Publisher:
Publish Date: 2001-09-01
Features: Model theory is an important branch of modern mathematics and has extensive applications in various fields such as function theory, Lie group representation theory, number theory, geometry, and communications. Model forms can be divided into two major categories: analytic and non-analytic. Analytic models originated in the 1920s and have now been fully developed, while non-analytic models are more recently developed and have significant applications in modern physics. These two types of models share similarities in many aspects, but the non-analytic case has its own unique challenges. This book begins with non-analytic modular forms on the upper half-plane and systematically introduces the theory and methods of trace formulas, particularly focusing on the research overview and achievements of modular forms both domestically and internationally, including the author's extensive research contributions. The book is divided into seven chapters, covering topics such as Maass cusp forms, Selberg trace formulas, trace formulas on GL(2), Kuznetsov trace formulas, relative trace formulas (geometric part), and relative trace formulas (spectrum decomposition part). An appendix introduces p-adic fields. To guide readers into this field as smoothly as possible and provide an understanding of modular forms and group representation theory in number theory, the book emphasizes the simplest cases of modular forms and trace formulas. This book can serve as a graduate textbook for mathematics majors in higher education institutions, as well as a reference for senior undergraduate students, young teachers, and mathematicians.