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Euclidean minima of algebraic number fields

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Abstract

In this paper, we use some of our previous results to improve an upper bound of Bayer–Fluckiger, Borello, and Jossen on the Euclidean minima of algebraic number fields. Our bound depends on the degree n of the field, its signature, discriminant, and the Hermite constant in dimension n.

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Notes

  1. See the latest 2023 version of this paper at arXiv:1511.00908v3 where some corrections in the proof of [2, Theorem 5.3] have been made.

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Acknowledgements

The authors are grateful to the referee for valuable comments. The authors also would like to thank Eva Bayer-Fluckiger, Martino Borello, and Peter Jossen for valuable discussions and especially for updating their paper [2]. During the preparation of this work, M. Sha was supported in part by the Guangdong Basic and Applied Basic Research Foundation, Grant 2022A1515012032, and I.E. Shparlinski by the Australian Research Council, Grants DP230100530 and DP230100534.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, 03225, Vilnius, Lithuania

    Artūras Dubickas

  2. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Min Sha

  3. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia

    Igor E. Shparlinski

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  1. Artūras Dubickas
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  2. Min Sha
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  3. Igor E. Shparlinski
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Correspondence to Min Sha.

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Dubickas, A., Sha, M. & Shparlinski, I.E. Euclidean minima of algebraic number fields. Arch. Math. 122, 405–414 (2024). https://doi.org/10.1007/s00013-023-01943-1

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