On p-Rationality of Cubic and Quartic Number Fields
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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