Ergodicity of the action of K* on A_K

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.

12 pages; minor changes

References in corpus (2)

• On Bost-Connes type systems for number fields
• Von Neumann algebras arising from Bost-Connes type systems

Cited by in corpus (1)

• Phase transitions on C*-algebras from actions of congruence monoids on rings of algebraic integers