Height Functions for Groups of $S$-units of Number Fields and Reductions Modulo Prime Ideals
Tom 63 / 2015
Bulletin Polish Acad. Sci. Math. 63 (2015), 25-31 MSC: Primary 11G50, 11R27; Secondary 11J68. DOI: 10.4064/ba63-1-4
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.