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Divisibility sequences of polynomials and heights estimates

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arxiv 1609.04750 v1 pith:OAOW6MXU submitted 2016-09-15 math.NT math.AG

Bartosz Naskręcki This is my paper · ORCID
classification math.NTmath.AG
keywords constantdivisibilitysequencesspecificboundscharacteristicchosencompute
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abstract

In this note we compute a constant $N$ that bounds the number of non--primitive divisors in elliptic divisibility sequences over function fields of any characteristic. We improve a result of Ingram--Mah{\'e}--Silverman--Stange--Streng, 2012, and we show that the constant can be chosen independently of the specific point and to some extent of the specific curve, as predicted in loc. cit.

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  1. Remarks on a theorem of Silverman

    math.NT 2026-07 accept novelty 5.5 of 10

    Silverman-type exact reduction orders hold for elliptic curves over global function fields (n coprime to p) and for abelian-scheme sections over C when the Betti map is generically submersive.

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