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Gitterpunkte in Lemniskatenscheiben

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Abstract

Let G (R) denote the number of lattice points (ξ,η)ε **Z2 in the domain B(R) bounded by the lemniscate (x2+y2)2=2R2 (x2−y2) and put P(R)=G(R)-R2(R2 being the area of B(R)). The purpose of this paper is to determine the order of magnitude of P(R) for large R by proving the asymptotic relation (3). An analogous result is given for the “eight curve” x4=R2 (x2−y2).

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Literatur

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Authors and Affiliations

  1. Institut für Mathematik und angewandte Statistik der Universität für Bodenkultur, Gregor Mendel-Straβe 33, A-1180, Wien, Österreich

    Werner Georg Nowak

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  1. Werner Georg Nowak
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Nowak, W.G. Gitterpunkte in Lemniskatenscheiben. Manuscripta Math 39, 277–285 (1982). https://doi.org/10.1007/BF01165792

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  • DOI: https://doi.org/10.1007/BF01165792

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