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Teitelbaum's exceptional zero conjecture in the function field case
-
Hilmar Hauer
and
Ignazio Longhi
Published/Copyright:
May 8, 2006
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 𝔭 and ∞, avoiding the construction of a 𝔭-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.
Received: 2005-01-13
Published Online: 2006-05-08
Published in Print: 2006-02-24
© Walter de Gruyter
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Articles in the same Issue
- Three-dimensional exponential sums with monomials
- A Fourier transformation for Higgs bundles
- Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane
- Kähler quantization and reduction
- Traces of Hecke operators acting on three-dimensional hyperbolic space
- Teitelbaum's exceptional zero conjecture in the function field case
- Symmetries, quotients and Kähler-Einstein metrics
- Smoothing of ribbons over curves
