Dynamical zeta functions and Kummer congruences

The Universal Kummer Congruences

Let p be a prime. In this paper, we present detailed p-adic analysis to factorials and double factorials and their congruences. We give good bounds for the p-adic sizes of the coefficients of the divided universal Bernoulli number B̂n n when n is divisible by p−1. Using these we then establish the universal Kummer congruences modulo powers of a prime p for the divided universal Bernoulli numbers...

Dynamical Zeta Functions

The study of periodic orbits for dynamical systems dates back to the very origins of the subject. Given a diieomorphism f : M ! M of a compact manifold it is a classical problem to count the number of periodic orbits fx; fx; : : : ; f n?1 xg, with f n x = x. For each n 1, we denote by N(n) the number of periodic points of period n. General Problem. What can we say about the numbers N(n)? What d...

Dynamical zeta functions

These notes are a rather subjective account of the theory of dynamical zeta functions. They correspond to three lectures presented by the author at the “Numeration” meeting in Leiden in 2010.

Zeta Functions and Dynamical Systems

In this brief note we present a very simple strategy to investigate dynamical determinants for uniformly hyperbolic systems. The construction builds on the recent introduction of suitable functional spaces which allow to transform simple heuristic arguments in rigorous ones. Although the results so obtained are not exactly optimal the straightforwardness of the argument makes it noticeable.

Kummer Type Congruences and Stickelberger Subideals