Far Eastern Mathematical Journal

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On the distribution of integer points

A. V. Ustinov

2009, issue 1-2, P. 176–181

Abstract

We study distribution of distances from primitive integer points to the origin.

Keywords: Kloosterman sums, integer lattice

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References

[1] V. A. Bykovskij, A. V Ustinov, “Statistika traektorij chastic dlya odnorodnoj dvumernoj modeli «Periodicheskij gaz Lorenca»”, Funkc. analiz i prilozheniya, 42:3 (2008), 10–22. [2] V. A. Bykovskij, A. V Ustinov, “Statistika traektorij chastic v neodnorodnoj zadache Sinaya dlya dvumernoj reshetki”, Izvestiya RAN, seriya matematicheskaya, 73:4 (2009), 17–36. [3] I. M. Vinogradov, Osnovy teorii chisel, Nauka, M., 1972. [4] A. V. Ustinov, “O chisle reshenij sravneniya xy?l(modq) pod grafikom dvazhdy nepreryvno differenciruemoj funkcii”, Algebra i analiz, 20:5 (2008), 186–216. [5] F. P. Boca, C. Cobeli, A. Zaharescu, “Distribution of lattice points visible from the origin”, Comm. Math. Phys., 20 (2000), 433–470. [6] T. Estermann, “On {K}loosterman's sum”, Mathematika, 8 (1961), 83–86.

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