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On norms of integers in a full module of an algebraic number field and the distribution of values of binary integral quadratic forms

Published online by Cambridge University Press:  26 February 2010

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

Let K be an algebraic number field. By a. full module in K [l,p.83] we mean a finitely-generated (necessarily free) subgroup M of the additive group of K whose rank is equal to the degree [K : ℚ] of K over the rational field ℚ. The intersection of M with ℤK, the ring of integers of K, is also a full module I, and we shall concern ourselves chiefly with the latter, in that we wish to count the number of rational integers in a given interval which can be expressed as the norms of elements of I. More precisely, we shall adapt the methods of [2] to prove the following

Type
Research Article
Information
Mathematika , Volume 22 , Issue 2 , December 1975 , pp. 108 - 111
Copyright
Copyright © University College London 1975

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References

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