This book 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.

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.

Presents an elementary introduction that requires only few pre-requisites Introduces a host of different techniques such as representation theory, adeles and ideles, and the methods of Tate's thesis Combines the classical and analytical viewpoint and the modern representation-theoretic approach and reveals their interplay Includes supplementary material: sn.pub/extras Includes supplementary material: sn.pub/extras

Autorentext

Anton Deitmar is a professor of Mathematics at the University of Tübingen, Germany. Siegfried Echterhoff is a professor of Mathematics at the University of Münster, Germany.

Inhalt

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.