2004/01/21 by Hilmar Hauer, Hauer, Hilmar, Ignazio Longhi +1
Mathematics · #11G05 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT #msc:11G05
paper · pdf · doi:10.48550/arxiv.math/0401276
31 pages
arxiv created 2004/01/21 · openalex publication_date 2004/01/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The exceptional zero conjecture relates the first derivative of the p-adic L-function of a rational elliptic curve with split multiplicative reduction at p to its complex L-function. Teitelbaum formulated an analogue of Mazur and Tate's refined (multiplicative) version of this conjecture for elliptic curves over the rational function field \FQ(T) with split multiplicative reduction at two places \fp and ∞, avoiding the construction of a \fp-adic L-function. This article proves Teitelbaum's conjecture up to roots of unity by developing Darmon's theory of double integrals over arbitrary function fields. A function field version of Darmon's period conjecture is also obtained.