Distribution Theorems of L-functions (Pitman Research Notes in Mathematics Series)

This Research Note discusses a variety of results which are, in the classical case of the Riemann zeta function, mostly due to Selberg. The first three chapters are completely expository -î the first chapter being entirely devoted to examples of various simple types of L-functions and their properties. The next three chapters extend some of Selberg's results to certain Langlands L-functions. In order to extend these results even further, to motivic L-functions, the last chapter is devoted to explicitly constructing a certain simple class of "automorphic/-adic motives" using algebraic geometry.
This book provides, as well as some background on simple L-functions, an introduction to work on Montgomery's pair correlation conjecture and the above-mentioned (mostly unpublished) work of Selberg.
Readership: Researchers and graduate students in analytic number theory and modular functions.