Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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

Authors: Michael Pohst and Hans Zassenhaus
Journal: Math. Comp. 31 (1977), 754-770
MSC: Primary 12A45
MathSciNet review: 0498486
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $ 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 \leqslant 7$.

References [Enhancements On Off] (What's this?)

  • [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] Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, PWN—Polish Scientific Publishers, Warsaw, 1974. Monografie Matematyczne, Tom 57. MR 0347767
  • [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] Hans Zassenhaus, On Hensel factorization. I, J. Number Theory 1 (1969), 291–311. MR 0242793,
  • [6] Hans Zassenhaus, On the units of orders, J. Algebra 20 (1972), 368–395. MR 0289469,
  • [7] Hans Zassenhaus, On the second round of the maximal order program, Applications of number theory to numerical analysis (Proc. Sympos., Univ. Montréal, Montreal, Que., 1971) Academic Press, New York, 1972, pp. 389–431. MR 0371862
  • [8] Hans Zassenhaus, Gauss’ theory of ternary quadratic forms, and example of the theory of homogeneous forms in many variables, with applications, Selected topics on ternary forms and norms (Sem. Number Theory, California Inst. Tech., Pasadena, Calif., 1974/75) California Inst. Tech., Pasadena, Calif., 1976, pp. 84. MR 0437458

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 12A45

Retrieve articles in all journals with MSC: 12A45

Additional Information

Article copyright: © Copyright 1977 American Mathematical Society