355 research outputs found
Dynamical zeta functions and Kummer congruences
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.Comment: 12 pages, AMS-LaTe
The n-th prime asymptotically
A new derivation of the classic asymptotic expansion of the n-th prime is
presented. A fast algorithm for the computation of its terms is also given,
which will be an improvement of that by Salvy (1994).
Realistic bounds for the error with \li^{-1}(n), after having retained the
first m terms, for , are given. Finally, assuming the Riemann
Hypothesis, we give estimations of the best possible such that, for , we have where is the sum of the first four terms
of the asymptotic expansion
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