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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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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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