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An extended inhomogeneous minimum

Published online by Cambridge University Press:  09 April 2009

E. S. Barnes
E. S. Barnes
Affiliation:
University of Adelaide, South Australia.
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Abstract

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A new arithmetic invariant E(f) is defined for integral binary quadratic forms f. It has the property that, denoting by fm the norm-form of a quadratic number field Q(m), E(fm) < 1 if and only if Q(m) has class number one.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 4 , December 1976 , pp. 431 - 441
Copyright
Copyright © Australian Mathematical Society 1976

References

Davenport, H., (1946) ‘Non-homogeneous binary quadratic forms’, Proc. K. Ned. Akad. van Wet. 49, 815–821.Google Scholar
Pollard, H., (1950) The theory of algebraic numbers (Math. Association of America, New York, 1950).Google Scholar