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Arithmetic properties of series of reciprocals of algebraic integers

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Abstract

We obtain results bounding the degree of the series \(\sum _{n=1}^{\infty } 1/\alpha _n\), where \(\{\alpha _n\}\) is a sequence of algebraic integers satisfying certain algebraic conditions and growth conditions. Our results extend results of Erdős, Hančl and Nair.

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Acknowledgements

We thank the referees for their helpful comments.

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  1. Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000, Aarhus C, Denmark

    S. B. Andersen & S. Kristensen

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  1. S. B. Andersen
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  2. S. Kristensen
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Correspondence to S. Kristensen.

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Communicated by Ilse Fischer.

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Andersen, S.B., Kristensen, S. Arithmetic properties of series of reciprocals of algebraic integers. Monatsh Math 190, 641–656 (2019). https://doi.org/10.1007/s00605-019-01326-1

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  • DOI: https://doi.org/10.1007/s00605-019-01326-1

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