منابع مشابه
Extending Nathanson Heights to Arbitrary Finite Fields
In this paper, we extend the definition of the Nathanson height from points in projective spaces over Fp to points in projective spaces over arbitrary finite fields. If [a0 : . . . : an] ∈ P(Fp), then the Nathanson height is hp([a0 : a1 : . . . : ad]) = min b∈Fp d ∑ i=0 H(bai) where H(ai) = |N(ai)|+p(deg(ai)−1) with N the field norm and |N(ai)| the element of {0, 1, . . . , p− 1} congruent to N...
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Let k be a number field, let θ be a nonzero algebraic number, and let H(·) be the Weil height on the algebraic numbers. In response to a question by T. Loher and D. W. Masser, we prove an asymptotic formula for the number of α ∈ k with H(αθ) ≤ X, and we analyze the leading constant in our asymptotic formula. In particular, we prove a sharp upper bound in terms of the classical Schanuel constant...
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Let K be a function field in one variable over an arbitrary field F. Given a rational function φ ∈ K(z) of degree at least two, the associated canonical height on the projective line was defined by Call and Silverman. The preperiodic points of φ all have canonical height zero; conversely, if F is a finite field, then every point of canonical height zero is preperiodic. However, if F is an infin...
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ژورنال
عنوان ژورنال: Bulletin de la Société mathématique de France
سال: 1979
ISSN: 0037-9484,2102-622X
DOI: 10.24033/bsmf.1905