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Lattice points on circles

Part of: Multiplicative number theory

Published online by Cambridge University Press:  09 April 2009

Javier Cilleruelo
Javier Cilleruelo
Affiliation:
Departmento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain e-mail: franciscojavier.cilleruelo@uam.es
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Abstract

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We prove that the lattice points on the circles x2 + y2 = n are well distributed for most circles containing lattice points.

MSC classification

Secondary: 11N36: Applications of sieve methods
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 2 , April 2002 , pp. 217 - 222
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Cilleruelo, J., ‘The distribution of the lattice points on circles’, J. Number Theory 43 (1993), 198–202.CrossRefGoogle Scholar
[2]Kubilyus, I., ‘The distribution of Gaussian primes in sectors and contours’, Leningrad. Gos. Univ. Uchen. Zap. Sen Mat. Nauk 137 (1950), 40–52.Google Scholar
[3]Mitsui, T., ‘Generalized prime number theorem’, Japan J. Math. 26 (1956), 1–42.CrossRefGoogle Scholar
[4]Nathanson, M., Additive number theory: the classical bases (Springer, New York, 1996).CrossRefGoogle Scholar