Involve: A Journal of Mathematics
- Volume 2, Number 1 (2009), 37-64.
Computing points of small height for cubic polynomials
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.
Involve, Volume 2, Number 1 (2009), 37-64.
Received: 25 September 2008
Revised: 25 November 2008
Accepted: 26 November 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11G50: Heights [See also 14G40, 37P30]
Secondary: 11S99: None of the above, but in this section 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]
Benedetto, Robert; Dickman, Benjamin; Joseph, Sasha; Krause, Benjamin; Rubin, Daniel; Zhou, Xinwen. Computing points of small height for cubic polynomials. Involve 2 (2009), no. 1, 37--64. doi:10.2140/involve.2009.2.37. https://projecteuclid.org/euclid.involve/1513799116