Higher Weight Heegner Points
| dc.creator | Hopkins, Kimberly | |
| dc.date | 2009-04-07 | |
| dc.date.accessioned | 2026-07-07T13:01:18Z | |
| dc.date.available | 2026-07-07T13:01:18Z | |
| dc.description | In this paper we formulate a conjecture which partially generalizes the Gross-Kohnen-Zagier theorem to higher weight modular forms. For f in S_k(N) satisfying certain conditions, we construct a map from the Heegner points of level N to a complex torus defined by f. We define higher weight analogues of Heegner divisors on this torus. We conjecture they all lie on a line, and their positions are given by the coefficients of a certain Jacobi form corresponding to f. In weight 2, our map is the modular parametrization map (restricted to Heegner points), and our conjectures are implied by Gross-Kohnen-Zagier. For any weight, we expect that our map is the Abel-Jacobi map on a certain modular variety, and so our conjectures are consistent with the conjectures of Beilinson-Bloch. We have verified our map is the Abel-Jacobi for weight 4. We provide numerical evidence to support our conjecture for a variety of examples. | |
| dc.identifier | https://arxiv.org/abs/0904.1141 | |
| dc.identifier | http://arxiv.org/abs/0904.1141 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226106 | |
| dc.subject | Number Theory | |
| dc.subject | 11G40; 11F67; 11F37 | |
| dc.title | Higher Weight Heegner Points | |
| dc.type | text |