On a representation of the idele class group related to primes and zeros of L-functions
Number Theory
2015-10-23 v3 Representation Theory
Abstract
Let K be a global field. Using natural spaces of functions on the adele ring and the idele class group of K, we construct a virtual representation of the idele class group of K whose character is equal to the Weil distribution that occurs in Andre Weil's Explicit Formula. Hence this representation encodes information about the distribution of the prime ideals of K, and it is a spectral interpretation for the poles and zeros of the L-function. It is closely related to the spectral interpretation of Alain Connes.
Keywords
Cite
@article{arxiv.math/0311468,
title = {On a representation of the idele class group related to primes and zeros of L-functions},
author = {Ralf Meyer},
journal= {arXiv preprint arXiv:math/0311468},
year = {2015}
}