On calculating the number N(D) of global cubic fields F of given discriminant D

2021 ◽  
Author(s):  
István Gaál ◽  
Michael Pohst
Keyword(s):  
Cubic Fields

scholarly journals Cubic Fields and Radical Extensions

2000 ◽  
Vol 107 (3) ◽  
pp. 254-256
Author(s):  
Ming-chang Kang
Keyword(s):  
Cubic Fields

The determination of units in totally real cubic fields

1960 ◽  
Vol 56 (4) ◽  
pp. 318-321 ◽  
Author(s):  
H. J. Godwin
Keyword(s):  
Trial And Error ◽  
Integral Lattice ◽  
Cubic Field ◽  
Cubic Fields ◽  
Trial And Error Method ◽  
Totally Real ◽  
Rational Integral ◽  
Fundamental Units ◽  
Error Method

The determination of a pair of fundamental units in a totally real cubic field involves two operations—finding a pair of independent units (i.e. such that neither is a power of the other) and from these a pair of fundamental units (i.e. a pair ε1; ε2 such that every unit of the field is of the form with rational integral m, n). The first operation may be accomplished by exploring regions of the integral lattice in which two conjugates are small or else by factorizing small primes and comparing different factorizations—a trial-and-error method, but often a quick one. The second operation is accomplished by obtaining inequalities which must be satisfied by a fundamental unit and its conjugates and finding whether or not a unit exists satisfying these inequalities. Recently Billevitch ((1), (2)) has given a method, of the nature of an extension of the first method mentioned above, which involves less work on the second operation but no less on the first.

scholarly journals A Converse of Artin′s Density Theorem: The Case of Cubic Fields

1993 ◽  
Vol 45 (1) ◽  
pp. 28-44 ◽  
Author(s):  
I. Delcorso ◽  
R. Dvornicich
Keyword(s):  
Density Theorem ◽  
Cubic Fields

The product of non-homogeneous linear forms. II The minimum of a class of non-homogeneous linear forms

1954 ◽  
Vol 50 (3) ◽  
pp. 380-390 ◽  
Author(s):  
P. A. Samet
Keyword(s):  
Linear Forms ◽  
Cubic Fields ◽  
Homogeneous Linear

In this paper we determine the first minimum of a class of linear forms associated with certain cubic fields that depend on a parameter.

scholarly journals Torsion of rational elliptic curves over cubic fields

2016 ◽  
Vol 46 (6) ◽  
pp. 1899-1917 ◽  
Author(s):  
Enrique González-Jiménez ◽  
Filip Najman ◽  
José M. Tornero
Keyword(s):  
Elliptic Curves ◽  
Cubic Fields

Cubic Fields

2018 ◽  
pp. 1-61
Author(s):  
Samuel A. Hambleton ◽  
Hugh C. Williams
Keyword(s):  
Cubic Fields

scholarly journals A fast algorithm to compute cubic fields

1997 ◽  
Vol 66 (219) ◽  
pp. 1213-1238 ◽  
Author(s):  
K. Belabas
Keyword(s):  
Fast Algorithm ◽  
Cubic Fields

scholarly journals The simplest cubic fields

1974 ◽  
Vol 28 (128) ◽  
pp. 1137-1137 ◽  
Author(s):  
Daniel Shanks
Keyword(s):  
Cubic Fields
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