Abstract
Let be a polynomial of degree at least two. The associated canonical height is a certain real-valued function on that returns zero precisely at preperiodic rational points of . Morton and Silverman conjectured in 1994 that the number of such points is bounded above by a constant depending only on . A related conjecture claims that at nonpreperiodic rational points, is bounded below by a positive constant (depending only on ) times some kind of height of itself. In this paper, we provide support for these conjectures in the case by computing the set of small height points for several billion cubic polynomials.
Citation
Robert Benedetto. Benjamin Dickman. Sasha Joseph. Benjamin Krause. Daniel Rubin. Xinwen Zhou. "Computing points of small height for cubic polynomials." Involve 2 (1) 37 - 64, 2009. https://doi.org/10.2140/involve.2009.2.37
Information