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Primitive lattice points in rational ellipses and related arithmetic functions

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Abstract

Assuming the Riemann Hypothesis to be true, an asymptotic with a sharp error term is established for the number of primitive lattice points inside a rational ellipseau 2+buv+cv 2≤x (a, b, c integers,b 2−4ac<0). A generalization of the result is given applying (as an example) to counting functions of Pythagorean triangles.

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  1. Institut für Mathematik, Universität für Bodenkultur, Gregor Mendel-Strasse 33, A-1180, Wien, Austria

    Werner Georg Nowak

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  1. Werner Georg Nowak
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Nowak, W.G. Primitive lattice points in rational ellipses and related arithmetic functions. Monatshefte für Mathematik 106, 57–63 (1988). https://doi.org/10.1007/BF01501488

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  • DOI: https://doi.org/10.1007/BF01501488

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