Analogies between analysis on foliated spaces and arithmetic geometry

Details Analogies between analysis on foliated spaces and arithmetic geometry Analogies between analysis on foliated spaces and arithmetic geometry

2007-09-18

arxiv.org/abs/0709.2801v1

Mathematics

Number Theory

to appear in a conference volume in honour of Hermann Weyl

Scientific paper

We point out analogies between (a) the explicit formulas in analytic number theory and transversal index theory, (b) Lichtenbaum's recent conjectures on special values of Hasse-Weil zeta functions and a formula for special values of Ruelle zeta functions, (c) work of Cramer on the zeroes of the Riemann zeta function and a result of Chazarain on the trace of a wave operator. These analogies suggest certain problems in the analysis on foliated spaces. The paper is mostly a review of previous work but the ideas concerning (c) are new.

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