English

On algebraic integers in short intervals and near smooth curves

Number Theory 2017-11-30 v3

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 α\alpha of height Q\leq Q in intervals of length depending on QQ.

Keywords

Cite

@article{arxiv.1602.01630,
  title  = {On algebraic integers in short intervals and near smooth curves},
  author = {Friedrich Götze and Anna Gusakova},
  journal= {arXiv preprint arXiv:1602.01630},
  year   = {2017}
}