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

Fabrizio Barroero

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

Number Theory 2014-09-12 v3

Authors: Fabrizio Barroero

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 $\bar{S}$ -integers of bounded height and fixed degree over $k$ , where $\bar{S}$ is the set of places of $\bar{k}$ lying above the ones in $S$ .

Keywords

algebraic $S$-integers number fields bounded height fixed degree asymptotic formula counting problems places of a field

Cite

@article{arxiv.1309.7849,
  title  = {Algebraic $S$-integers of fixed degree and bounded height},
  author = {Fabrizio Barroero},
  journal= {arXiv preprint arXiv:1309.7849},
  year   = {2014}
}

Comments

arXiv admin note: text overlap with arXiv:1305.0482, accepted for publication on Acta Arithmetica

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

Abstract

Keywords

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