The hyperbola $xy = N$

Javier Cilleruelo; Jorge Jiménez-Urroz

doi:10.5802/jtnb.267

The hyperbola

x y = N

Javier Cilleruelo; Jorge Jiménez-Urroz

Journal de Théorie des Nombres de Bordeaux, Volume 12 (2000) no. 1, pp. 87-92.

Abstract
Résumé

We include several results providing bounds for an interval on the hyperbola $x y = N$ containing $k$ lattice points.

On montre plusieurs résultats à propos de la longueur minimale d’un arc de l’hyperbole $x y = N$ contenant $k$ points entiers.

MR: 1827840 | Zbl: 1006.11055

DOI: 10.5802/jtnb.267

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     title = {The hyperbola $xy = N$},
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     publisher = {Universit\'e Bordeaux I},
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Javier Cilleruelo; Jorge Jiménez-Urroz. The hyperbola $xy = N$. Journal de Théorie des Nombres de Bordeaux, Volume 12 (2000) no. 1, pp. 87-92. doi : 10.5802/jtnb.267. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.267/

References
Cited by

[1] J. Cilleruelo, A. Córdoba, Trigonometric polynomials and lattice points. Proc. Amer. Math. Soc. 115 (1992), 899-905. | MR: 1089403 | Zbl: 0777.11035

[2] J. Cilleruelo, J. Jiménez-Urroz, Divisors in a Dedekind domain. Acta. Arith. 85 (1998), 229-233. | MR: 1627827 | Zbl: 0910.11043

[3] A. Granville, J. Jiménez-Urroz, The least common multiple and lattice points on hyperbolas. To appear in Quart. J. Math. | MR: 1782098 | Zbl: 0983.11058

[4] G.H. Hardy, E.M. Wright, Introduction to the theory of numbers. Clarendon Press. 4th ed., Oxford, 1960. | MR: 568909 | Zbl: 0086.25803

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