Geodesic
Nielsen zeta function, 3-manifolds, and asymptotic expansions in Nielsen theory
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 312-329

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We prove that the Nielsen zeta function is a rational function or a radical of a rational function for orientation- preserving homeomorphisms on closed orientable 3-dimensional manifolds which are special Haken or Seifert manifolds. In the case of pseudo-Anosov homeomorphism of surface we compute an asymptotics for the number of twisted conjugacy classes or for the number of Nielsen fixed point classes whose norm is at most $x$. 
@article{ZNSL_2000_266_a16,
     author = {A. L. Fel'shtyn},
     title = {Nielsen zeta function, 3-manifolds, and  asymptotic expansions in {Nielsen} theory},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {312--329},
     publisher = {mathdoc},
     volume = {266},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a16/}
}
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A. L. Fel'shtyn. Nielsen zeta function, 3-manifolds, and  asymptotic expansions in Nielsen theory. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 312-329. http://geodesic.mathdoc.fr/item/ZNSL_2000_266_a16/