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arXiv · 1602.01630

On algebraic integers in short intervals and near smooth curves

Friedrich Götze·Anna Gusakova
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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 $α$ of height $\leq Q$ in intervals of length depending on $Q$.

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Friedrich Götze, Anna Gusakova. 2017-02-28. On algebraic integers in short intervals and near smooth curves. https://doi.org/10.4064/aa8333-2-2017

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