On small discriminants of number fields of degree 8 and 9

2019/10/16 by Battistoni, Francesco · 1 citation
#11R21 #11R29 #11Y40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1910.07208

Abstract

We classify all the number fields with signature (4,2), (6,1), (1,4) and (3,3) having discriminant lower than a specific upper bound. This completes the search for minimum discriminants for fields of degree 8 and continues it in the degree 9 case. We recall the theoretical tools and the algorithmic steps upon which our procedure is based, then we focus on the novelties due to a new implementation of this process on the computer algebra system PARI/GP; finally, we make some remarks about the final results, among which the existence of a number field with signature (3,3) and small discriminant which was not previously known.

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