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Mathematics > Number Theory

arXiv:math/0401276 (math)
[Submitted on 21 Jan 2004]

Title:Teitelbaum's exceptional zero conjecture in the function field case

Authors:Hilmar Hauer, Ignazio Longhi
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Abstract: 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 $\infty$, 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.
Comments: 31 pages
Subjects: Number Theory (math.NT)
MSC classes: 11G05
Cite as: arXiv:math/0401276 [math.NT]
  (or arXiv:math/0401276v1 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.math/0401276

Submission history

From: Hilmar Hauer [view email]
[v1] Wed, 21 Jan 2004 17:33:10 UTC (20 KB)
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