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Height Functions for Groups of S-units of Number Fields and Reductions Modulo Prime Ideals

Stefan Barańczuk — 2015

Bulletin of the Polish Academy of Sciences. Mathematics

A result on the orders of the reductions of an element of the group of S-units of a number field is obtained by investigating three height functions for groups of S-units of number fields which are analogous to local, global and canonical height functions for elliptic curves.

A remark on certain simultaneous divisibility sequences

Stefan Barańczuk; Piotr Rzonsowski — 2014

Colloquium Mathematicae

We investigate possible orders of reductions of a point in the Mordell-Weil groups of certain abelian varieties and in direct products of the multiplicative group of a number field. We express the result obtained in terms of divisibility sequences.

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