Value at 2 of the L-function of an elliptic curve
| dc.creator | Brunault, Francois | |
| dc.date | 2006-02-09 | |
| dc.date.accessioned | 2026-07-07T07:03:15Z | |
| dc.date.available | 2026-07-07T07:03:15Z | |
| dc.description | We study the special value at 2 of L-functions of modular forms of weight 2 on congruence subgroups of the modular group. We prove an explicit version of Beilinson's theorem for the modular curve X_1(N). When N is prime, we deduce that the target space of Beilinson's regulator map is generated by the images of Milnor symbols associated to modular units of X_1(N). We also suggest a reformulation of Zagier's conjecture on L(E,2) for the jacobian J_1(N) of X_1(N), where E is an elliptic curve of conductor N. In this direction we define an analogue of the elliptic dilogarithm for any jacobian J : it is a function R_J from the complex points of J to a finite-dimensional vector space. In the case J=J_1(N), we establish a link between the aforementioned L-values and the function R_J evaluated at \Q-rational points of the cuspidal subgroup of J. | |
| dc.description | 155 pages, PhD thesis, French, with an appendix by Loic Merel | |
| dc.identifier | https://arxiv.org/abs/math/0602186 | |
| dc.identifier | http://arxiv.org/abs/math/0602186 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108905 | |
| dc.subject | Number Theory | |
| dc.subject | 11F67 | |
| dc.title | Value at 2 of the L-function of an elliptic curve | |
| dc.type | text |