Teitelbaum's exceptional zero conjecture in the function field case
| dc.creator | Hauer, Hilmar | |
| dc.creator | Longhi, Ignazio | |
| dc.date | 2004-01-21 | |
| dc.date.accessioned | 2026-07-07T05:04:44Z | |
| dc.date.available | 2026-07-07T05:04:44Z | |
| dc.description | 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. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/0401276 | |
| dc.identifier | http://arxiv.org/abs/math/0401276 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69918 | |
| dc.subject | Number Theory | |
| dc.subject | 11G05 | |
| dc.title | Teitelbaum's exceptional zero conjecture in the function field case | |
| dc.type | text |