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Let φ ∈ [ޑz] be a polynomial of degree d at least two. The associated canonical heightĥ φ is a certain real-valued function on ޑ that returns zero precisely at preperiodic rational points of φ. 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 nonpreperiodic rational points,ĥ φ is bounded below by a positive constant (depending only on d) times some kind of height of φ itself. Indoi:10.2140/involve.2009.2.37 fatcat:zqukkhgewzegdnml6n2wgsbgfy