On Totally Real Cubic Fields with Discriminant $D < 10^7

The authors have constructed a table of the 592923 nonconjugate totally real cubic number fields of discriminant $D < 10^7$, thereby extending the existing table of fields with $D < 5 \times 10^5$ constructed by Ennola and Turunen [4]. Each field is given by its discriminant and the coefficien...

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Bibliographic Details
Published in:Mathematics of computation 1988-04, Vol.50 (182), p.581-594, Article 581
Main Authors: Llorente, Pascual, Quer, Jordi
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic value
Discriminants
Integers
Mathematical congruence
Mathematical tables
Mathematics
Polynomials
Zero
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Summary:The authors have constructed a table of the 592923 nonconjugate totally real cubic number fields of discriminant $D < 10^7$, thereby extending the existing table of fields with $D < 5 \times 10^5$ constructed by Ennola and Turunen [4]. Each field is given by its discriminant and the coefficients of a generating polynomial. The method used is an improved version of the method developed in [8]. The article contains an exposition of the modified method, statistics and examples. The decomposition of the rational primes is studied and the relative frequency of each type of decomposition is compared with the corresponding density given by Davenport and Heilbronn [2].
ISSN:0025-5718
1088-6842
DOI:10.2307/2008626