Geodesic
The Reidemeister and Nielsen zeta functions
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 6, Tome 167 (1988), pp. 164-168 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we formulate a rationality theorem for the Reidemeister and Nielsen zeta-functions modulo a normal subgroup of the fundamental group. We give conditions under which these zeta-functions coincide. We formulate a conjecture aboutentropy for the Reidemeister numbers. We show that the radius of convergence of the Nielsen zeta-function for an orientation-preserving homeomorphism $f$ of a compact surface is an invariant of a three-dimensional manifold, the torus of the map $f$, and a special flow on it. In special cases we derive a functional equation for the Nielsen zeta-function. We give an example of a transcendental Nielsen zeta function. 
@article{ZNSL_1988_167_a12,
     author = {A. L. Fel'shtyn},
     title = {The {Reidemeister} and {Nielsen} zeta functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {164--168},
     year = {1988},
     volume = {167},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_167_a12/}
}
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A. L. Fel'shtyn. The Reidemeister and Nielsen zeta functions. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 6, Tome 167 (1988), pp. 164-168. http://geodesic.mathdoc.fr/item/ZNSL_1988_167_a12/