Nonvanishing of L-values and the Weyl law

• 成果类型: Article
• 署名作者: Luo, WZ
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062104
• 发表日期: 2001
• 页码: 477-502
• 关键词: cusp forms; rank

摘要

This work is concerned with the validity of Weyl law for hyperbolic surfaces on the asymptotic counting of the Laplace eigenvalues. Following Phillips-Sarnak, we show that Weyl law is false for generic hyperbolic surfaces under the standard multiplicity assumption by establishing that a positive proportion of certain critical values of Rankin-Selberg L-functions do not vanish.