Dynamical zeta functions and Kummer congruences

Details Dynamical zeta functions and Kummer congruences Dynamical zeta functions and Kummer congruences

2003-09-11

arxiv.org/abs/math/0309190v1

Mathematics

Number Theory

12 pages, AMS-LaTeX

Scientific paper

We establish a connection between the coefficients of Artin-Mazur zeta-functions and Kummer congruences. This allows to settle positively the question of the existence of a map T such that the number of fixed points of the n-th iterate of T is equal to the absolute value of the 2n-th Euler number. Also we solve a problem of Gabcke related to the coefficients of Riemann-Siegel formula.

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