Geodesic
Algebraic $S$-integers of fixed degree and bounded height
Fabrizio Barroero1
1 Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa, Italy
Acta Arithmetica, Tome 167 (2015) no. 1, pp. 67-90.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $S$.
DOI : 10.4064/aa167-1-4
Keywords: number field finite set places nbsp containing archimedean count number algebraic points bounded height whose coordinates lie ring s integers moreover asymptotic formula number overline integers bounded height fixed degree where overline set places overline lying above nbsp

Fabrizio Barroero 1

1 Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa, Italy 
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Fabrizio Barroero. Algebraic $S$-integers of fixed degree and bounded height. Acta Arithmetica, Tome 167 (2015) no. 1, pp. 67-90. doi : 10.4064/aa167-1-4. http://geodesic.mathdoc.fr/articles/10.4064/aa167-1-4/

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