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

DOI:
https://doi.org/10.1090/S0025-5718-1977-0498486-5

MathSciNet review:
0498486

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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 linear inequalities for one unknown each. Application is made to the unit search for all totally real number fields of minimal discriminant for .

**[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**, https://doi.org/10.1016/0022-314X(69)90047-X**[6]**Hans Zassenhaus,*On the units of orders*, J. Algebra**20**(1972), 368–395. MR**0289469**, https://doi.org/10.1016/0021-8693(72)90064-6**[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**

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DOI:
https://doi.org/10.1090/S0025-5718-1977-0498486-5

Article copyright:
© Copyright 1977
American Mathematical Society