On special zeros of p-adic L-functions of Hilbert modular forms

• 成果类型: Article
• 署名作者: Spiess, Michael
• 署名单位: University of Bielefeld
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0465-0
• 发表日期: 2014
• 页码: 69-138
• 关键词: representations; COHOMOLOGY

摘要

Let E be a modular elliptic curve over a totally real number field F. We prove the weak exceptional zero conjecture which links a (higher) derivative of the p-adic L-function attached to E to certain p-adic periods attached to the corresponding Hilbert modular form at the places above p where E has split multiplicative reduction. Under some mild restrictions on p and the conductor of E we deduce the exceptional zero conjecture in the strong form (i.e. where the automorphic p-adic periods are replaced by the -invariants of E defined in terms of Tate periods) from a special case proved earlier by Mok. Crucial for our method is a new construction of the p-adic L-function of E in terms of local data.