Algebraic S-integers of fixed degree and bounded height

2013/09/30 by Fabrizio Barroero, Barroero, Fabrizio
Mathematics · #11R04 #FOS: Mathematics #Number Theory (math.NT) #Primary 11G50 #math.NT #msc:11G50 #msc:11R04

paper · pdf · doi:10.48550/arxiv.1309.7849

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

arxiv created 2014/09/11 · arxiv updated 2014/09/12

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

Citations

• Counting algebraic integers of fixed degree and bounded height

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