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

2012/07/10 by Michael Spieß, Michael Spiess, Spiess, Michael · 2 citations
Mathematics · #11F41 #11F67 #11F70 #11G40 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F41 #msc:11F67 #msc:11F70 #msc:11G40

paper · pdf · doi:10.48550/arxiv.1207.2289

openalex publication_date 2012/07/10 · arxiv created 2013/01/17 · arxiv updated 2013/01/18 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

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 \cL-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.

Cited by

• Periods of modular forms and applications to the conjectures of Oda and of Prasanna-Venkatesh
• p-adic L-functions of automorphic forms and exceptional zeros

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