Arithmetic L-functions

Loosely speaking, arithmetic L-functions are those Dirichlet series with appropriate functional equations and Euler products which should satisfy a Riemann Hypothesis. Selberg has given specific requirements which seem likely to make this definition precise. Arithmetic L-functions arise in many situations: from the representation theory of groups associated with number fields, from automorphic forms on arithmetic groups acting on symmetric spaces, and from the harmonic analysis on these spaces.

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