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On the angular distribution of Gaussian integers with fixed norm. (English) Zbl 1044.11073
Summary: We study the distribution of lattice points \(a + 1b\) on the fixed circle \(a^2 + b^2 = n\). 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.

11K31 Special sequences
11P21 Lattice points in specified regions
Full Text: DOI
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