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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On totally real cubic fields

Authors: Veikko Ennola and Reino Turunen
Journal: Math. Comp. 44 (1985), 495-518
MSC: Primary 11R16; Secondary 11-04, 11R29, 11Y40
MathSciNet review: 777281
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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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Article copyright: © Copyright 1985 American Mathematical Society