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The lattice point discrepancy of a torus in ℝ3

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Abstract

This article provides an asymptotic formula for the number of integer points in the three-dimensional body

$$ \left( \begin{gathered} x \hfill \\ y \hfill \\ z \hfill \\ \end{gathered} \right) = t\left( \begin{gathered} (a + r\cos \alpha )\cos \beta \hfill \\ (a + r\cos \alpha )\sin \beta \hfill \\ r\sin \alpha \hfill \\ \end{gathered} \right),0 \leqq \alpha ,\beta < 2\pi ,0 \leqq r \leqq b, $$

for fixed a > b > 0 and large t.

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Authors and Affiliations

  1. Institute of Mathematics, Department of Integrative Biology, Universität für Bodenkultur Wien, Gregor Mendel-Straße 33, 1180, Wien, Österreich

    W. G. Nowak

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  1. W. G. Nowak
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Correspondence to W. G. Nowak.

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The author gratefully acknowledges support from the Austrian Science Fund (FWF) under project Nr. P18079-N12.

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Nowak, W.G. The lattice point discrepancy of a torus in ℝ3 . Acta Math Hung 120, 179–192 (2008). https://doi.org/10.1007/s10474-007-7129-8

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  • DOI: https://doi.org/10.1007/s10474-007-7129-8

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