Cubic, quartic and sextic Pólya fields

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