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On algebraic integers in short intervals and near smooth curves

Volume 179 / 2017

Friedrich Götze, Anna Gusakova 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 $Q$.

Authors

  • Friedrich GötzeUniversity of Bielefeld
    Bielefeld, Germany
    e-mail
  • Anna GusakovaUniversity of Bielefeld
    Bielefeld, Germany
    e-mail

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