In 1970 A. Baker and W. Schmidt introduced regular systems of numbers and vectors, showing that the set of real algebraic numbers forms a regular system on any fixed interval. This fact was used to prove several important results in the metric theory of transcendental numbers. In this paper the concept of a regular system is applied to the set of algebraic integers of height $\leq Q$ in intervals of length depending on $Q$.
Keywords:
baker schmidt introduced regular systems numbers vectors showing set real algebraic numbers forms regular system fixed interval prove several important results metric theory transcendental numbers paper concept regular system applied set algebraic integers height leq intervals length depending nbsp
@article{10_4064_aa8333_2_2017,
author = {Friedrich G\"otze and Anna Gusakova},
title = {On algebraic integers in short intervals and near smooth curves},
journal = {Acta Arithmetica},
pages = {251--265},
year = {2017},
volume = {179},
number = {3},
doi = {10.4064/aa8333-2-2017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8333-2-2017/}
}
TY - JOUR
AU - Friedrich Götze
AU - Anna Gusakova
TI - On algebraic integers in short intervals and near smooth curves
JO - Acta Arithmetica
PY - 2017
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VL - 179
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UR - http://geodesic.mathdoc.fr/articles/10.4064/aa8333-2-2017/
DO - 10.4064/aa8333-2-2017
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%J Acta Arithmetica
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%V 179
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/aa8333-2-2017/
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Friedrich Götze; Anna Gusakova. On algebraic integers in short intervals and near smooth curves. Acta Arithmetica, Tome 179 (2017) no. 3, pp. 251-265. doi: 10.4064/aa8333-2-2017
