On the generation of the coefficient field of a newform by a single Hecke eigenvalue
| dc.creator | Koo, Koopa Tak-Lun | |
| dc.creator | Stein, William | |
| dc.creator | Wiese, Gabor | |
| dc.date | 2007-11-21 | |
| dc.date | 2008-02-25 | |
| dc.date.accessioned | 2026-07-07T09:22:43Z | |
| dc.date.available | 2026-07-07T09:22:43Z | |
| dc.description | Let f be a non-CM newform of weight k > 1. Let L be a subfield of the coefficient field of f. We completely settle the question of the density of the set of primes p such that the p-th coefficient of f generates the field L. This density is determined by the inner twists of f. As a particular case, we obtain that in the absence of non-trivial inner twists, the density is 1 for L equal to the whole coefficient field. We also present some new data on reducibility of Hecke polynomials, which suggest questions for further investigation. | |
| dc.description | 13 pages, more complete result, some corollaries added | |
| dc.identifier | https://arxiv.org/abs/0711.3405 | |
| dc.identifier | http://arxiv.org/abs/0711.3405 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155474 | |
| dc.subject | Number Theory | |
| dc.subject | 11F30 (Primary); 11F11, 11F25, 11F80, 11R45 (Secondary) | |
| dc.title | On the generation of the coefficient field of a newform by a single Hecke eigenvalue | |
| dc.type | text |