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Number theory and dynamical systems on foliated spaces

Christopher Deninger
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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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Christopher Deninger. 2002-04-10. Number theory and dynamical systems on foliated spaces. https://arxiv.org/abs/math/0204110

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