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On lattice points in the domain |xy | ≤1, | x + y | ≤√5, and applications to asymptotic formulae in lattice point theory (II)

Published online by Cambridge University Press:  24 October 2008

K. Mahler
K. Mahler
Affiliation:
Mathematics DepartmentManchester University
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Extract

I. Lattice points in the domain | x |α + | y |α ≤ 1

Theorem 4. Let G be the star domain

where α > 0. Then, when α tends to zero,

Proof. The linear substitution

changes G into the similar domain

and so

.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 40 , Issue 2 , June 1944 , pp. 116 - 120
Copyright
Copyright © Cambridge Philosophical Society 1944

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