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On fundamental units of real quadratic fields of class number 1

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Abstract

In this paper, we give a nontrivial lower bound for the fundamental unit of norm \(-1\) of a real quadratic field of class number 1.

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Acknowledgements

We thank Professor Yasuhiro Kishi for comments which improved the quality of the paper. We are very grateful to the referee for pointing out several important mistakes in previous versions of the paper. The second author would like to thank the Max Planck Institute for Mathematics, Bonn for hospitality and support during the period when this paper was written. The first author was supported by the Croatian Science Foundation under the Project No. 6422 and the QuantiXLie Center of Excellence, a project cofinanced by the Croatian Government and European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme (Grant KK.01.1.1.01.0004). The second author was supported in part by NRF (South Africa) Grants CPRR160325161141 and an A-rated researcher award and by CGA (Czech Republic) Grant 17-02804S.

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Correspondence to Andrej Dujella.

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Dujella, A., Luca, F. On fundamental units of real quadratic fields of class number 1. Arch. Math. 113, 349–353 (2019). https://doi.org/10.1007/s00013-019-01355-0

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  • DOI: https://doi.org/10.1007/s00013-019-01355-0

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