Foliations and Number Theory
by
Christopher Deninger
Universität Münster, Fachbereich Mathematik, Einsteinstr.62, 48149 Münster, Germany

After reviewing basic properties of leafwise cohomology for foliations we explain recent progress in the theory of dynamical trace formulas for one-codimensional foliations. We then compare these trace formulas with certain classical formulas in analytic number theory and discuss similarities and differences. Finally we explain how to generalize the foliation setting in such a way that the two types of formulas should become identical. In simple examples this has been checked. The considerations derive their interest from the fact that in the foliation setting an analogue of the Riemann conjecture can be proved.

Paper reference: arXiv:math.NT/0204110

Date received: March 20, 2001