Ergodicity of the Action of K* on
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Publication:2927909
DOI10.1093/IMRN/RNT114zbMATH Open1315.46080arXiv1211.3256OpenAlexW3106070356MaRDI QIDQ2927909
Jeffrey C. Lagarias, Sergey Neshveyev
Publication date: 5 November 2014
Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1211.3256
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Measure-preserving transformations (28D05) Zeta functions and (L)-functions of number fields (11R42) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)
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