On totally real cubic fields with discriminant 𝐷<10⁷

Llorente, Pascual; Quer, Jordi

doi:10.1090/S0025-5718-1988-0929555-8

On totally real cubic fields with discriminant $D<10^ 7$
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by Pascual Llorente and Jordi Quer PDF

Math. Comp. 50 (1988), 581-594 Request permission

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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Cursos, Seminarios y Tesis del PEAM

P. Llorente and A. V. Oneto, On the real cubic fields, Math. Comp. 39 (1982), no. 160, 689–692. MR 669661, DOI 10.1090/S0025-5718-1982-0669661-3

Jour. de Math.

I. O. Angell, A table of totally real cubic fields, Math. Comput. 30 (1976), no. 133, 184–187. MR 0401701, DOI 10.1090/S0025-5718-1976-0401701-6