## On algebraic integers in short intervals and near smooth curves

### Volume 179 / 2017

Acta Arithmetica 179 (2017), 251-265
MSC: Primary 11J13; Secondary 11J83, 11R04.
DOI: 10.4064/aa8333-2-2017
Published online: 11 July 2017

#### Abstract

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 $Q$.