Automorphic Forms

Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiless proof of Fermats 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.

Doubly periodic functions.-Modular forms for SL2(Z).-Representations of SL2(R).-p-adic numbers.-Adeles and ideles.-Tate’s thesis.-Automorphic representations of GL2(A).-Automorphic L-functions.