We obtain an arithmetic expression of the Selberg zeta function
for cocompact Fuchsian group defined via an indefinite division
quaternion algebra over $\mathbf{Q}$. As application to the
prime geodesic theorem, we prove certain uniformity of the
distribution.
Publié le : 2002-09-14
Classification:
Quaternion algebra,
Selberg zeta function,
Prime geodesic theorem,
11R52,
11M72,
58E10
@article{1148392633,
author = {Arakawa, Tsuneo and Koyama, Shin-ya and Nakasuji, Maki},
title = {Arithmetic forms of Selberg zeta functions with applications to prime geodesic theorem},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {78},
number = {10},
year = {2002},
pages = { 120-125},
language = {en},
url = {http://dml.mathdoc.fr/item/1148392633}
}
Arakawa, Tsuneo; Koyama, Shin-ya; Nakasuji, Maki. Arithmetic forms of Selberg zeta functions with applications to prime geodesic theorem. Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, pp. 120-125. http://gdmltest.u-ga.fr/item/1148392633/