Integral points of fixed degree and bounded height

2013/09/08 by Martin Widmer, Widmer, Martin
Mathematics · #11G35 #FOS: Mathematics #Number Theory (math.NT) #Primary 11R04 #Secondary 11G50 #math.NT #msc:11G35 #msc:11G50 #msc:11R04

paper · pdf · doi:10.48550/arxiv.1309.1944

to appear in Int. Math. Res. Notices

arxiv created 2015/08/17 · arxiv updated 2015/08/18

Abstract

By Northcott's Theorem there are only finitely many algebraic points in affine n-space of fixed degree over a given number field and of height at most X. For large X the asymptotics of these cardinalities have been investigated by Schanuel, Schmidt, Gao, Masser and Vaaler, and the author. In this paper we study the case where the coordinates of the points are restricted to algebraic integers, and we derive the analogues of Schanuel's, Schmidt's, Gao's and the author's results.

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