Let k be a number field and S a finite set of places of k containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of S-integers of k. Moreover, we give an asymptotic formula for the number of S̅-integers of bounded height and fixed degree over k, where S̅ is the set of places of k̅ lying above the ones in S.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-1-4,
author = {Fabrizio Barroero},
title = {Algebraic S-integers of fixed degree and bounded height},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {67-90},
zbl = {06390255},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-1-4}
}
Fabrizio Barroero. Algebraic S-integers of fixed degree and bounded height. Acta Arithmetica, Tome 168 (2015) pp. 67-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-1-4/