Mollification of the fourth moment of automorphic L-functions and arithmetic applications

• 成果类型: Article
• 署名作者: Kowalski, E; Michel, P; VanderKam, J
• 署名单位: Princeton University; Universite de Montpellier; Institut Universitaire de France; Center for Communications & Computing
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220000086
• 发表日期: 2000
• 页码: 95-151
• 关键词: divisor problem; heegner points; l-series; derivatives; zeros; rank

摘要

We compute the asymptotics of twisted fourth power moments of modular L-functions of large prime level near the critical line. This allows us to prove some new non-vanishing results on the central values of automorphic L-functions, in particular those obtained by base change from GL(2)(Q) to GL(2)(K) for K a cyclic field of low degree.