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arXiv · 2304.10157

On $ p-$Rationality of Cubic and Quartic Number Fields

Hang Li·Derong Qiu
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Abstract

In this paper, a new criterion is given to determine the $p-$rationality of some complex cubic number fields in terms of $ p-$divisibility of certain terms of a third-order recurrence sequence, several illustrated examples are constructed,the relations between generalized $ abc-$conjecture and the $p-$rationality are discussed, from which some explicit fields satisfying Greenberg's Generalized Conjecture (GGC, for short) are obtained.

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Hang Li, Derong Qiu. 2023-04-20. On $ p-$Rationality of Cubic and Quartic Number Fields. https://doi.org/10.1142/s1793042126500582

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