Sur le rang de J_0(q)
| dc.creator | Kowalski, Emmanuel | |
| dc.creator | Michel, Philippe | |
| dc.date | 1997-07-31 | |
| dc.date.accessioned | 2026-07-07T09:15:48Z | |
| dc.date.available | 2026-07-07T09:15:48Z | |
| dc.description | In this paper, we prove an unconditionnal bound for the analytic rank (i.e the order of vanishing at the critical point of the $L$ function) of the new part $J^n_0(q)$, of the jacobian of the modular curve $X_0(q)$. Our main resultis the following upper bound: for $q$ prime, one has $$rank_a(J_0^n(q))\ll \dim J_0^n(q)$$ where the implied constant is absolute. All previously known non trivials bounds of $rank_a(J_0^n(q))$ assumed the generalized Riemann hypothesis; here, our proof is unconditionnal, and is based firstly on the construction by Perelli and Pomykala of a new test function in the context of Riemann-Weil explicit formulas, and secondly on a density theorem for the zeros of $L$ functions attached to new forms. | |
| dc.identifier | https://arxiv.org/abs/math/9707237 | |
| dc.identifier | http://arxiv.org/abs/math/9707237 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153144 | |
| dc.subject | Number Theory | |
| dc.title | Sur le rang de J_0(q) | |
| dc.type | text |