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Mathematics of Computation

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On totally real cubic fields with discriminant $ D<10\sp 7$

Authors: Pascual Llorente and Jordi Quer
Journal: Math. Comp. 50 (1988), 581-594
MSC: Primary 11R16; Secondary 11Y40
MathSciNet review: 929555
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Abstract: 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].

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Keywords: Real cubic fields
Article copyright: © Copyright 1988 American Mathematical Society