Automorphic Forms

✍ Scribed by Anton Deitmar (auth.)

• Publisher: Springer-Verlag London
• Year: 2012
• Tongue: English
• Leaves: 262
• Series: Universitext
• Edition: 1
• Category: Library

✦ Synopsis

Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.

✦ Table of Contents

Front Matter....Pages I-IX
Doubly Periodic Functions....Pages 1-13
Modular Forms for SL 2 (ℤ)....Pages 15-77
Representations of SL 2 (ℝ)....Pages 79-103
p -Adic Numbers....Pages 105-121
Adeles and Ideles....Pages 123-141
Tate’s Thesis....Pages 143-161
Automorphic Representations of $\mathrm{GL}_{2}(\mathbb {A})$ ....Pages 163-209
Automorphic L-Functions....Pages 211-240
Back Matter....Pages 241-252

✦ Subjects

Mathematics, general; Number Theory; Group Theory and Generalizations; Algebra