Vanishing of L-functions of elliptic curves over number fields
| dc.creator | David, Chantal | |
| dc.creator | Fearnley, Jack | |
| dc.creator | Kisilevsky, Hershy | |
| dc.date | 2004-06-01 | |
| dc.date.accessioned | 2026-07-07T05:08:46Z | |
| dc.date.available | 2026-07-07T05:08:46Z | |
| dc.description | Let $E$ be an elliptic curve over $\mathbb{Q}$, with L-function $L_E(s)$. For any primitive Dirichlet character $χ$, let $L_E(s, χ)$ be the L-function of $E$ twisted by $χ$. In this paper, we use random matrix theory to study vanishing of the twisted L-functions $L_E(s, χ)$ at the central value $s=1$. In particular, random matrix theory predicts that there are infinitely many characters of order 3 and 5 such that $L_E(1, χ)=0$, but that for any fixed prime $k \geq 7$, there are only finitely many character of order $k$ such that $L_E(1, χ)$ vanishes. With the Birch and Swinnerton-Dyer Conjecture, those conjectures can be restated to predict the number of cyclic extensions $K/\mathbb{Q}$ of prime degree such that $E$ acquires new rank over $K$. | |
| dc.identifier | https://arxiv.org/abs/math/0406012 | |
| dc.identifier | http://arxiv.org/abs/math/0406012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71397 | |
| dc.subject | Number Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 11G40 | |
| dc.title | Vanishing of L-functions of elliptic curves over number fields | |
| dc.type | text |