Distribution of prime ideals and the space of adele classes

Sergey Neshveyev (U Oslo)

Wednesday 6th March, 2013 16:00-17:00 204


The space A_K/K* of adele classes for a global field K was used by Connes to give a spectral interpretation of critical zeros of Hecke L-functions. It is known that this space is quite tricky. The precise statement for K=Q is that the action of Q* on A_Q is ergodic, so from the classical point of view A_Q/Q* consists of just one point. I will explain why the same is true for any global field and how this is related to a generalized prime number theorem. (Joint work with J. Lagarias)

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