Ergodicity of the action of K* on A_K
Number Theory
2015-09-21 v2 Dynamical Systems
Operator Algebras
Abstract
Connes gave a spectral interpretation of the critical zeros of zeta- and L-functions for a global field K using a space of square integrable functions on the space A_K/K* of adele classes. It is known that for K=Q the space A_K/K* cannot be understood classically, or in other words, the action of Q* on A_Q is ergodic. We prove that the same is true for any global field K, in both the number field and function field cases.
Keywords
Cite
@article{arxiv.1211.3256,
title = {Ergodicity of the action of K* on A_K},
author = {Jeffrey C. Lagarias and Sergey Neshveyev},
journal= {arXiv preprint arXiv:1211.3256},
year = {2015}
}
Comments
12 pages; minor changes