On totally real cubic fields

Ennola, Veikko; Turunen, Reino

doi:10.1090/S0025-5718-1985-0777281-8

On totally real cubic fields
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by Veikko Ennola and Reino Turunen PDF

Math. Comp. 44 (1985), 495-518 Request permission

Abstract:

The authors have constructed a table of the 26440 nonconjugate totally real cubic number fields of discriminant $D < 500000$ thereby extending the existing table of fields with $D < 100000$ by I. O. Angell [1]. Serious defects in Angell’s table are pointed out. For each field, running number, discriminant, coefficients of a generating polynomial, integral basis, class number, and a fundamental pair of units are listed. The article contains statistics about the following subjects: distribution of class numbers; fields in which every norm-positive unit is totally positive; nonconjugate fields with the same discriminant; fields with noncyclic class group. The fields are tabulated by means of a method due to Davenport and Heilbronn [7], [8] which leads to a unique normalized generating polynomial. The given units are chosen so that the fundamental parallelogram of the unit lattice determined by the corresponding vectors in the logarithmic space is reduced.

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