DISTRIBUTION OF EIGENVALUES FOR THE MODULAR GROUP

Authors
BOGOMOLNY E LEYVRAZ F SCHMIT C
Citation
E. Bogomolny et al., DISTRIBUTION OF EIGENVALUES FOR THE MODULAR GROUP, Communications in Mathematical Physics, 176(3), 1996, pp. 577-617
Citations number
43
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Communications in Mathematical Physics → ACNP
ISSN journal
00103616
Volume
176
Issue
3
Year of publication
1996
Pages
577 - 617
Database
ISI
SICI code
0010-3616(1996)176:3<577:DOEFTM>2.0.ZU;2-9
Abstract
The two-point correlation functions of energy levels for free motion o n the modular domain, both with periodic and Dirichlet boundary condit ions, are explicitly computed using a generalization of the Hardy-Litt lewood method. It is shown that in the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distributio n but they have prominent number-theoretical oscillations at larger sc ale. The results agree well with numerical simulations.