Hostname: page-component-7dd5485656-kp629 Total loading time: 0 Render date: 2025-10-31T17:21:49.883Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Borevič, Z. I. and Šafarevič, I. R.. Number theory (Academic Press, New York, 1966).Google Scholar
2.Odoni, R. W. K.. “On the norms of algebraic integers”, Mathematika, 22 (1975), 71–80.CrossRefGoogle Scholar
3.Cohn, H.. A second course in number theory (Wiley, New York, 1962), chapters XII and XIII.Google Scholar
4.Landau, E.. Handbuch der Primzahlverteilung (Teubner, Leipzig, 1909), vol. 2, 643–644Google Scholar
5.Bernays, P.. “Über die Darstellung … durch primitiven binaren quadratischen Formen” (Dissertation, Gttingen, 1912).Google Scholar
6.Pall, G.. “The distribution of integers represented by binary quadratic forms”, Bull. Amer. Math. Soc, 49 (1943), 447–449CrossRefGoogle Scholar