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The Number of Lattice Points Above the Catenary

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Abstract

For fixed c > 1 and for arbitrary and independent a,b ≧ 1 let Z 2|b( cosh(x/a)−c) ≦ y < 0}. We investigate the asymptotic behaviour of R(a,b) for a,b → ∞. In the special case b = o(a 5/6) the lattice rest has true order of magnitude \(\frac{a}{{\sqrt b }}\).

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References

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  1. Institut für Mathematik U.A.St., Universität für Bodenkultur, A-1180, Wien, Austria

    G. Kuba

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  1. G. Kuba
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Kuba, G. The Number of Lattice Points Above the Catenary. Acta Mathematica Hungarica 87, 173–178 (2000). https://doi.org/10.1023/A:1006737403738

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