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Automorphic L-Functions

  • Anton Deitmar
Chapter
Part of the Universitext book series (UTX)

Abstract

In this chapter the adelic interpretation of modular forms is used to give an adelic description of their L-functions, which, as a byproduct, are vastly generalized. These general automorphic L-functions are defined as Euler products, the factor at a prime p is obtained from a p-adic representation, using the so called Satake Transformation. The analytic continuation of the L-function is obtained as an application of the Poisson Summation Formula. At the end of the chapter it finally is shown that this new, much more general construction of L-functions is compatible with the definitions of Chap.  3.

Keywords

Modular Form Trace Formula Algebra Homomorphism Double Coset Irreducible Unitary Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Anton Deitmar
    • 1
  1. 1.Inst. MathematikUniversität TübingenTübingenGermany

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