Automorphic Forms Beyond $\mathrm {GL}_2$ : Lectures from the 2022 Arizona Winter School (Mathematical Surveys and Monographs)

Eischen, Ellen Elizabeth/ Gan, Wee Teck/ Pollack, Aaron

American Mathematical Society（2024/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 187 p.
• 言語 ENG
• 商品コード 9781470474928
• DDC分類 512.7

Full Description

The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on ""Automorphic Forms beyond GL(2)"", held March 5-9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.

Contents

E. E. Eischen, Automorphic forms on unitary groups
Wee Teck Gan, Automorphic forms and the theta correspondence
Aaron Pollack, Modular forms on exceptional groups
Zhiwei Yun, Rigidity method for automorphic forms over function fields