Nonvanishing of L-values and the Weyl law

Authors
Luo, WZ
Citation
Wz. Luo, Nonvanishing of L-values and the Weyl law, ANN MATH, 154(2), 2001, pp. 477-502
Citations number
20
Categorie Soggetti
Mathematics
Journal title
ANNALS OF MATHEMATICS
ISSN journal
0003486X → ACNP
Volume
154
Issue
2
Year of publication
2001
Pages
477 - 502
Database
ISI
SICI code
0003-486X(200109)154:2<477:NOLATW>2.0.ZU;2-Y
Abstract
This work is concerned with the validity of Weyl law for hyperbolic surface s on the asymptotic counting of the Laplace eigenvalues. Following Phillips -Sarnak, we show that Weyl law is false for generic hyperbolic surfaces und er the standard multiplicity assumption by establishing that a positive pro portion of certain critical values of Rankin-Selberg L-functions do not van ish.