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On the norms of algebraic integers

Published online by Cambridge University Press:  26 February 2010

R. W. K. Odoni
R. W. K. Odoni
Affiliation:
Department of Mathematics, University of Exeter.
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Extract

In [1], the author considered the distribution of rational integers which are norms of elements of a given algebraic number field K, and in particular obtained the result

where A(K), B(K) and C(K) are positive parameters depending only on K, as does the implied constant in the O-term. In fact 0 < B(K) < 1, and B(K) is a rational number related to the Galois groups Gal and Gal, where is the normal hull of .

Type
Research Article
Information
Mathematika , Volume 22 , Issue 1 , June 1975 , pp. 71 - 80
Copyright
Copyright © University College London 1975

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References

1. Odoni, R.. “The Farey density of norm subgroups of global fields (I)”, Mathematika, 20 (1973), 155–169.CrossRefGoogle Scholar
2. Odoni, R.. “On a problem of Narkiewicz”, J. reine angew. Math, (to appear).Google Scholar
3. Titchmarsh, E. C.. The Theory of Functions (2nd ed., Oxford U.P., 1939), 157–159.Google Scholar
4. Hasse, H.. Bericht über neuere Untersuchungen … algebraischen Zahlkörper, (Physika-Verlag, Würzburg, 1970), Teil 2.Google Scholar
5. Kubilius, J.. Probabilistic methods in the theory of numbers, (American Mathematical Society Translations of Mathematical Monographs, vol. XL, 1964).Google Scholar