Divisibility sequences of polynomials and heights estimates

Bartosz Naskrecki

Divisibility sequences of polynomials and heights estimates

Bartosz Naskrecki

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Abstract

In this note we compute a constant N that bounds the number of nonprimitive divisors in elliptic divisibility sequences over function fields of any characteristic. We improve a result of Ingram– Mahé–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.

Original language	English
Pages (from-to)	989-1020
Number of pages	32
Journal	New York Journal of Mathematics
Volume	22
Publication status	Published - 17 Sept 2016

Keywords

Elliptic divisibility sequence
primitive divisor
elliptic surface
height of point

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via New York Journal of Mathematics at http://nyjm.albany.edu/j/2016/22-46.html. Please refer to any applicable terms of use of the publisher.
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http://nyjm.albany.edu/j/2016/22-46.html

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title = "Divisibility sequences of polynomials and heights estimates",

abstract = " In this note we compute a constant N that bounds the number of nonprimitive 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.",

keywords = "Elliptic divisibility sequence, primitive divisor, elliptic surface, height of point",

author = "Bartosz Naskrecki",

year = "2016",

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language = "English",

volume = "22",

pages = "989--1020",

journal = "New York Journal of Mathematics",

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T1 - Divisibility sequences of polynomials and heights estimates

AU - Naskrecki, Bartosz

PY - 2016/9/17

Y1 - 2016/9/17

N2 - In this note we compute a constant N that bounds the number of nonprimitive divisors in elliptic divisibility sequences over function fields of any characteristic. We improve a result of Ingram– Mahé–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.

AB - In this note we compute a constant N that bounds the number of nonprimitive divisors in elliptic divisibility sequences over function fields of any characteristic. We improve a result of Ingram– Mahé–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.

KW - Elliptic divisibility sequence

KW - primitive divisor

KW - elliptic surface

KW - height of point

M3 - Article (Academic Journal)

SN - 1076-9803

VL - 22

SP - 989

EP - 1020

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

ER -

Divisibility sequences of polynomials and heights estimates

Abstract

Keywords

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