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.
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Deitmar, A. (2013). Automorphic L-Functions. In: Automorphic Forms. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-4435-9_8
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DOI: https://doi.org/10.1007/978-1-4471-4435-9_8
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