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Fibonacci numbers and real quadratic p-rational fields

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Abstract

We characterize p-rational real quadratic fields in terms of generalized Fibonacci numbers. We then use this characterization to give numerical evidence to a conjecture of Greenberg asserting the existence of p-rational multi-quadratic fields of arbitrary degree \(2^{t}\), \(t\ge 1\).

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Acknowledgements

I would like to thank my advisor J. Assim for his guidance and patience during the preparation of this paper. Many thanks goes to H. Cohen and B. Abombert for their help on pariGP computations during the Atelier pariGP in Besançon. I also thank the referee for a careful reading of the manuscript and for several suggestions which improved the presentation of this paper.

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  1. University Moulail Ismail of Meknes, Marjane 2, BP: 298, Meknes, Morocco

    Zakariae Bouazzaoui

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  1. Zakariae Bouazzaoui
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Correspondence to Zakariae Bouazzaoui.

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Bouazzaoui, Z. Fibonacci numbers and real quadratic p-rational fields. Period Math Hung 81, 123–133 (2020). https://doi.org/10.1007/s10998-020-00320-7

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