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On the angular distribution of Gaussian integers with fixed norm |
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| Authors: | P. Erd s,R. R. Hall |
| Affiliation: | a Mathematical Institute, Hungarian Academy of Sciences, Budapest, P.O. Box 127, H. 1364, Hungary b Mathematics Department, University of York, Heslington, York YO1 5DD, UK |
| Abstract: | We study the distribution of lattice points a + 1b on the fixed circle a2 + b2 = n. Our results apply p.p. to the representable integers n, and we supply bounds for the discrepancy of the distribution, and for the maximum and minimum of the angles between consecutive points. As a corollary, we are able to show that when n is representable then it is almost surely representable with min(a, b) small, with an explicit bound. |
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