Octic 2-adic fields
This paper is the continuation of two previous works of the authors [J. Symb. Comput. 41, No. 1, 80--97 (2006; Zbl 1140.11350); Buell, Duncan (ed.), Algorithmic number theory. 6th international symposium, ANTS-VI, Burlington, VT, USA, June 13--18, 2004. Proceedings. Berlin: Springer. Lecture Notes in Computer Science 3076, 293--308 (2004; Zbl 1125.11356)]. The first one describes the interactive database of the authors of low degree \(p\)-adic fields, located at \url{http://math.la.asu.edu/?jj/localfields} and explains why low degree \(p\)-adic fields warrant a detailed investigation. The second one, treats the case of nonic 3-adic fields, finding 795 isomorphism classes and determines associated invariants of these classes. In this paper, in a parallel way to the second one, the authors study octic 2-adic fields and find that there are 1823 of them up to isomorphism. They compute the associated Galois group of each field, slopes measuring wild ramification and some other associated invariants. The authors present several tables that summarize complete information available in their online database.
scientific article; zbMATH DE number 5285722
scientific article