Cubic, quartic and sextic Polya fields

JOURNAL OF NUMBER THEORY

卷:133

Article

Leriche, Amandine^1,2 

[1] Ecole Cent Lille, F-59650 Villeneuve Dascq, France

[2] Univ Picardie Jules Verne, F-80039 Amiens, France

关键词: Cubic fields;    Quartic fields;    Sextic fields;    Polya fields;    Integer-valued polynomials;   

DOI  :  10.1016/j.jnt.2012.06.016

来源: Elsevier

【 摘 要 】

A Polya field is a number field K, with ring of integers O-K, such that the O-K-module formed by the integer-valued polynomials on O-K has a regular basis. We are interested here by Polya fields of small degree. We give a complete characterization of cyclic cubic, quartic and sextic Polya fields (quadratic Polya fields are known for a long time). Moreover, we prove that, with few exceptions, the compositum of two quadratic Polya fields is a biquadratic Polya field. Finally, we study sextic Polya fields which are the Galoisian closure of pure cubic fields. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free