New York Journal of Mathematics
Volume 22 (2016) 989-1020


Bartosz Naskręcki

Divisibility sequences of polynomials and heights estimates

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Published: September 17, 2016
Keywords: Elliptic divisibility sequence, primitive divisor, elliptic surface, height of point
Subject: Primary 11G05; Secondary 11B83 11C08 14H52.

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.


The author was supported by the National Science Centre Poland research grant 2012/07/B/ST1/03541 and by the DFG grant Sto299/11-1 within the framework of the Priority Programme SPP 1489.

Author information

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland, and School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK