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Hill, Jason B.

Mathematics

2006

MS

An algorithm is created to find the totally real quintic number field(s) of smallest field discriminant satisfying a given property. This algorithm is efficient and improves upon current number field table building techniques in the sense that only computations on totally real fields are ever considered. The algorithm is then used to locate totally real quintic number fields of all signature group ranks, including the first known instance of a field with a totally positive system of fundamental units.