Number theory and dynamical systems on foliated spaces

2002/04/10 by Christopher Deninger · 1 citation
Mathematics · #math.NT #math.DG #math.DS #msc:11-02 #msc:11R42 #msc:34C25 #msc:37C27 #msc:53C12 #msc:58B34

paper · pdf

published as Jber. d. Dt. Math.-Verein. 103 (2001), 79-100

arxiv created 2002/04/10 · arxiv updated 2009/11/30

Abstract

We discuss analogies between number theory and the theory of dynamical systems on spaces with a one-codimensional foliation. The emphasis is on comparing the "explicit formulas" of analytic number theory with certain dynamical Lefschetz trace formulas. We also point out a possible relation between an Arakelov-Euler characteristic and an Euler characteristic in the sense of Connes. Finally the role of generalized solenoids as phase spaces in our picture is explained.

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