Abstract

In recent years, there has been a lot of interest in the study of arithmetical and geometrical problems by means of the analytic properties of the associated $L$-functions. Roughly speaking, an $L$-function is a Dirichlet series, formed from local data at primes, which extends meromorphically to the complex plane. It is known that most of the $L$-functions in number theory share some basic analytic properties, in particular, meromorphic continuation, an Euler product and a functional equation. This general lecture is intended to provide an introduction to the analytic theory of $L$-functions from the viewpoint of classical distribution problems.



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