Gitterpunkte in Lemniskatenscheiben |
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Authors: | Werner Georg Nowak |
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Institution: | (1) Institut für Mathematik und angewandte Statistik der Universität für Bodenkultur, Gregor Mendel-Strae 33, A-1180 Wien, Österreich |
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Abstract: | Let G (R) denote the number of lattice points (,) **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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