Spectral expansions of overconvergent modular functions
| dc.creator | Loeffler, David | |
| dc.date | 2007-01-05 | |
| dc.date | 2007-05-28 | |
| dc.date.accessioned | 2026-07-07T08:55:24Z | |
| dc.date.available | 2026-07-07T08:55:24Z | |
| dc.description | The main result of this paper is an instance of the conjecture made by Gouvea and Mazur (Math. Res. Lett., 1995) which asserts that for certain values of r the space of r-overconvergent p-adic modular forms of tame level N and weight k should be spanned by the finite slope Hecke eigenforms. Using methods adapted from the work of Buzzard and Calegari I show that for p=2, k = 0, N = 1, this holds for all r in (5/12, 7/12). The proof relies on a certain factorisation of the U_p operator which is known in this case but I conjecture also holds for p = 3 and 5; this conjecture also implies exact formulae for the set of slopes similar to those proved for p=2 by Buzzard and Calegari. The same methods also provide an efficient approach to explicit computations of q-expansions of small slope overconvergent eigenforms, extending the computations of Gouvea and Mazur. | |
| dc.description | Updated version fixing some minor typos | |
| dc.identifier | https://arxiv.org/abs/math/0701168 | |
| dc.identifier | http://arxiv.org/abs/math/0701168 | |
| dc.identifier | International Mathematics Research Notices Vol. 2007 no. 16 (rnm050) | |
| dc.identifier | doi:10.1093/imrn/rnm050 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146262 | |
| dc.subject | Number Theory | |
| dc.subject | 11F33 | |
| dc.title | Spectral expansions of overconvergent modular functions | |
| dc.type | text |