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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The computation of a certain metric invariant of an algebraic number field


Author: Horst Brunotte
Journal: Math. Comp. 38 (1982), 627-632
MSC: Primary 12A99; Secondary 12-04, 12A45
MathSciNet review: 645677
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Abstract: 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.


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

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0645677-8
PII: S 0025-5718(1982)0645677-8
Article copyright: © Copyright 1982 American Mathematical Society