Computing All Power Integral Bases of Cubic Fields

1989 ◽  
Vol 53 (188) ◽  
pp. 689 ◽  
Author(s):  
I. Gaal ◽  
N. Schulte
Keyword(s):  
Integral Bases ◽  
Cubic Fields

scholarly journals Computing all power integral bases of cubic fields

1989 ◽  
Vol 53 (188) ◽  
pp. 689-689
Author(s):  
I. Ga{ál ◽  
N. Schulte
Keyword(s):  
Integral Bases ◽  
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.

A Note to the Paper on Integral Bases

1958 ◽  
Vol 9 (1) ◽  
pp. 173
Author(s):  
Virginia Hanly ◽  
H. B. Mann
Keyword(s):  
Integral Bases

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

Power Integral Bases in Composits of Number Fields

1998 ◽  
Vol 41 (2) ◽  
pp. 158-165 ◽  
Author(s):  
István Gaál
Keyword(s):  
Number Fields ◽  
Parametric Family ◽  
Prime Degree ◽  
Index Form ◽  
Form Equation ◽  
Integral Bases ◽  
Quadratic Extensions ◽  
Totally Real

AbstractIn the present paper we consider the problem of finding power integral bases in number fields which are composits of two subfields with coprime discriminants. Especially, we consider imaginary quadratic extensions of totally real cyclic number fields of prime degree. As an example we solve the index form equation completely in a two parametric family of fields of degree 10 of this type.

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
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