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Number theory and dynamical systems on foliated spaces | | Christopher Deninger
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10 Apr 2002 | | Journal: | Jber. d. Dt. Math.-Verein. 103 (2001), 79-100 | | Subject: | Number Theory; Differential Geometry; Dynamical Systems MSC-class: 11-02; 11R42; 34C25; 37C27; 53C12; 58B34 | math.NT math.DG math.DS | | 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. | | Source: | arXiv, math.NT/0204110 | | Services: | Forum | Review | PDF | Favorites | |
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