  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.
