Computing points of small height for cubic polynomials

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dc.creatorBenedetto, Robert L.
dc.creatorDickman, Benjamin
dc.creatorJoseph, Sasha
dc.creatorKrause, Benjamin
dc.creatorRubin, Daniel
dc.creatorZhou, Xinwen
dc.date2008-07-03
dc.date2008-12-03
dc.date.accessioned2026-07-07T12:08:30Z
dc.date.available2026-07-07T12:08:30Z
dc.descriptionLet f in Q[z] be a polynomial of degree d at least two. The associated canonical height \hat{h}_f is a certain real-valued function on Q that returns zero precisely at preperiodic rational points of f. Morton and Silverman conjectured in 1994 that the number of such points is bounded above by a constant depending only on d. A related conjecture claims that at non-preperiodic rational points, \hat{h}_f is bounded below by a positive constant (depending only on d) times some kind of height of f itself. In this paper, we provide support for these conjectures in the case d=3 by computing the set of small height points for several billion cubic polynomials.
dc.descriptionFinal version, to appear in Involve. 20 pages
dc.identifierhttps://arxiv.org/abs/0807.0468
dc.identifierhttp://arxiv.org/abs/0807.0468
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209339
dc.subjectNumber Theory
dc.subjectDynamical Systems
dc.subject11G50; 11S99, 37F10
dc.titleComputing points of small height for cubic polynomials
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