Open Access
Translator Disclaimer
2007 Splitting density for lifting about discrete groups
Yasufumi Hashimoto, Masato Wakayama
Tohoku Math. J. (2) 59(4): 527-545 (2007). DOI: 10.2748/tmj/1199649873


We study splitting densities of primitive elements of a discrete subgroup of a connected non-compact semisimple Lie group of real rank one with finite center in another larger such discrete subgroup. When the corresponding cover of such a locally symmetric negatively curved Riemannian manifold is regular, the densities can be easily obtained from the results due to Sarnak or Sunada. Our main interest is a case where the covering is not necessarily regular. Specifically, for the case of the modular group and its congruence subgroups, we determine the splitting densities explicitly. As an application, we study analytic properties of the zeta function defined by the Euler product over elements consisting of all primitive elements which satisfy a certain splitting law for a given lifting.


Download Citation

Yasufumi Hashimoto. Masato Wakayama. "Splitting density for lifting about discrete groups." Tohoku Math. J. (2) 59 (4) 527 - 545, 2007.


Published: 2007
First available in Project Euclid: 6 January 2008

zbMATH: 1148.11026
MathSciNet: MR2404204
Digital Object Identifier: 10.2748/tmj/1199649873

Primary: 11M36
Secondary: 11F72

Keywords: congruence subgroup , prime geodesic theorem , regular cover , Selberg's zeta function , Semisimple Lie groups , splitting density

Rights: Copyright © 2007 Tohoku University


Vol.59 • No. 4 • 2007
Back to Top