On the generation of the coefficient field of a newform by a single Hecke eigenvalue

dc.creatorKoo, Koopa Tak-Lun
dc.creatorStein, William
dc.creatorWiese, Gabor
dc.date2007-11-21
dc.date2008-02-25
dc.date.accessioned2026-07-07T09:22:43Z
dc.date.available2026-07-07T09:22:43Z
dc.descriptionLet 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.description13 pages, more complete result, some corollaries added
dc.identifierhttps://arxiv.org/abs/0711.3405
dc.identifierhttp://arxiv.org/abs/0711.3405
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155474
dc.subjectNumber Theory
dc.subject11F30 (Primary); 11F11, 11F25, 11F80, 11R45 (Secondary)
dc.titleOn the generation of the coefficient field of a newform by a single Hecke eigenvalue
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