Exceptional units in a family of quartic number fields-Reference-Cited by-同舟云学术

Exceptional units in a family of quartic number fields

Published:1998 Issue:222 Volume:67 Page:759-772
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Niklasch G.,Smart N.

Abstract

We determine all exceptional units among the elements of certain groups of units in quartic number fields. These groups arise from a one-parameter family of polynomials with two real roots.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1998-67-222/S0025-5718-98-00958-2/S0025-5718-98-00958-2.pdf

Reference16 articles.

1. Graduate Texts in Mathematics;Cohen, Henri,1993

2. Cubic number fields with exceptional units;Ennola, V.,1991

3. Formes linéaires en deux logarithmes et déterminants d’interpolation;Laurent, Michel;J. Number Theory,1995

4. Euclidean number fields of large degree;Lenstra, H. W., Jr.;Invent. Math.,1976

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