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Mathematics | Automorphic Forms

Automorphic Forms

Series: Universitext

Deitmar, Anton

2012, IX, 252 p. 2 illus.

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  • 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

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.

Content Level » Graduate

Keywords » Tate's thesis - automorphic L-functions - modular forms - tensor product theorem

Related subjects » Algebra - Mathematics - Number Theory and Discrete Mathematics

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