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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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The computation of a certain metric invariant of an algebraic number field
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by Horst Brunotte PDF
Math. Comp. 38 (1982), 627-632 Request permission


Let F be an algebraic number field and denote by $N(a)$ the absolute norm and by $\tilde {a}$ the maximum of the absolute values of the conjugates of the element a of F. Define ${c_F}$ to be the best possible constant with the property: For every $a \in F$ there exists a unit u of F such that $\widetilde {ua} \leqslant {c_F}N{(a)^{1/[F:{\mathbf {Q}}]}}$. An algorithm for the computation of ${c_F}$ is described and some examples are given.
    W. E. H. Berwick, "Algebraic number fields with two independent units," Proc. London Math. Soc., v. 34, 1932, pp. 360-378. S. I. Borewicz & I. R. Šafarevič, Zahlentheorie, Birkhäuser, Basel-Stuttgart, 1966.
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  • Donald E. Knuth, The art of computer programming. Vol. 2: Seminumerical algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0286318
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 38 (1982), 627-632
  • MSC: Primary 12A99; Secondary 12-04, 12A45
  • DOI:
  • MathSciNet review: 645677