  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.

Number Theory;Dynamical Systems