Algebraic $S$-integers of fixed degree and bounded height
Volume 167 / 2015
Acta Arithmetica 167 (2015), 67-90
MSC: Primary 11G50, 11R04.
DOI: 10.4064/aa167-1-4
Abstract
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 $\overline {S }$-integers of bounded height and fixed degree over $k$, where $\overline {S }$ is the set of places of ${\overline k}$ lying above the ones in $S$.
