On $ p-$Rationality of Cubic and Quartic Number Fields
Number Theory
2026-04-24 v3
Abstract
In this paper, a new criterion is given to determine the rationality of some complex cubic number fields in terms of divisibility of certain terms of a third-order recurrence sequence, several illustrated examples are constructed,the relations between generalized conjecture and the rationality are discussed, from which some explicit fields satisfying Greenberg's Generalized Conjecture (GGC, for short) are obtained.
Keywords
Cite
@article{arxiv.2304.10157,
title = {On $ p-$Rationality of Cubic and Quartic Number Fields},
author = {Hang Li and Derong Qiu},
journal= {arXiv preprint arXiv:2304.10157},
year = {2026}
}
Comments
10 pages