On $ p-$Rationality of Cubic and Quartic Number Fields
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911617178927104 |
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| author | Li, Hang Qiu, Derong |
| author_facet | Li, Hang Qiu, Derong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10157 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $ p-$Rationality of Cubic and Quartic Number Fields Li, Hang Qiu, Derong Number Theory 11R23, 11R29 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. |
| title | On $ p-$Rationality of Cubic and Quartic Number Fields |
| topic | Number Theory 11R23, 11R29 |
| url | https://arxiv.org/abs/2304.10157 |