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Algebraic $S$-integers of fixed degree and bounded height

Volume 167 / 2015

Fabrizio Barroero Acta Arithmetica 167 (2015), 67-90 MSC: Primary 11G50, 11R04. DOI: 10.4064/aa167-1-4


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 $S$.


  • Fabrizio BarroeroScuola Normale Superiore
    Piazza dei Cavalieri 7
    56126 Pisa, Italy

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