An effective number geometric method of computing the fundamental units of an algebraic number field-Reference-Cited by-同舟云学术

An effective number geometric method of computing the fundamental units of an algebraic number field

Published:1977 Issue:139 Volume:31 Page:754-770
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Pohst Michael,Zassenhaus Hans

Abstract

The Minkowski method of unit search is applied to particular types of parallelotopes permitting to discover algebraic integers of bounded norm in a given algebraic number field of degree n at will by solving successively 2 n 2n linear inequalities for one unknown each. Application is made to the unit search for all totally real number fields of minimal discriminant for n ⩽ 7 n \leqslant 7 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1977-31-139/S0025-5718-1977-0498486-5/S0025-5718-1977-0498486-5.pdf

Reference8 articles.

1. P. G. L. DIRICHLET, "Zur Theorie der complexen Einheiten," Mathematische Werke, Band II, reprint, Chelsea, New York, 1969, pp. 642-644. MR 40 #2514.

2. Monografie Matematyczne, Tom 57;Narkiewicz, Władysław,1974

3. H. MINKOWSKI, "Diskontinuitätsbereich für arithmetische Äquivalenz," J. Reine Angew. Math., v. 129, 1905, pp. 220-274.

4. M. POHST, "The minimum discriminant of seventh degree totally real algebraic number fields," Algebra and Number Theory. Special volume, Academic Press.

5. On Hensel factorization. I;Zassenhaus, Hans;J. Number Theory,1969

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