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On the region defined by | xy | ≤ 1, x2 + y2 ≤ t

Published online by Cambridge University Press:  24 October 2008

Kathleen Ollerenshaw
Kathleen Ollerenshaw
Affiliation:
11 Elm RoadManchester 20
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Extract

In this paper I find the critical lattices of the region Kt defined by the inequalities | xy | ≤ 1, x2 + y2 ≤ t (t > 0). I deduce in §9 the arithmetic minima of a pair of binary quadratic forms

where f1 is indefinite, f2 is positive definite, and f1, f2 are harmonically related, that is to say

and

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 1 , January 1953 , pp. 63 - 71
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Mahler, K.Proc. Lond. math. Soc. (2), 49 (1946), 128–57.CrossRefGoogle Scholar
(2)Mahler, K.Proc. roy. Soc. A, 187 (1946), 151–87.Google Scholar
(3)Ollerenshaw, K.Proc. Comb. phil. Soc. 41 (1945), 77–96.CrossRefGoogle Scholar
(4)Ollerenshaw, K.J. Lond. math. Soc. 23 (1948), 148–53.CrossRefGoogle Scholar