In this paper we describe how to use the algorithmic methods provided by Hunter and Pohst in order to give a complete classification of number fields of degree 8 and signature (2,3) with absolute discriminant less than a certain bound. The choice of this bound comes from the local corrections given by prime ideals to the lower estimates for discriminants obtained with the Odlyzko–Poitou–Serre method.
Battistoni, F., The minimum discriminant of number fields of degree 8 and signature (2,3), <<JOURNAL OF NUMBER THEORY>>, 2019; 198 (N/A): 386-395. [doi:10.1016/j.jnt.2018.09.007] [https://hdl.handle.net/10807/270254]
The minimum discriminant of number fields of degree 8 and signature (2,3)
Battistoni, Francesco
2019
Abstract
In this paper we describe how to use the algorithmic methods provided by Hunter and Pohst in order to give a complete classification of number fields of degree 8 and signature (2,3) with absolute discriminant less than a certain bound. The choice of this bound comes from the local corrections given by prime ideals to the lower estimates for discriminants obtained with the Odlyzko–Poitou–Serre method.
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