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arXiv · 1211.3256

Ergodicity of the action of K* on A_K

Jeffrey C. Lagarias·Sergey Neshveyev
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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.

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Jeffrey C. Lagarias, Sergey Neshveyev. 2013-06-08. Ergodicity of the action of K* on A_K. https://doi.org/10.1093/imrn%2Frnt114

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