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, Tome 12 (2000) no. 1, pp. 87-92

Abstract (VO)
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 Zbl

DOI : 10.5802/jtnb.267

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     author = {Javier Cilleruelo and Jorge Jim\'enez-Urroz},
     title = {The hyperbola $xy = N$},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {87--92},
     year = {2000},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {1},
     doi = {10.5802/jtnb.267},
     zbl = {1006.11055},
     mrnumber = {1827840},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.267/}
}

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Javier Cilleruelo; Jorge Jiménez-Urroz. The hyperbola $xy = N$. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 1, pp. 87-92. doi: 10.5802/jtnb.267

Bibliographie
Cité par

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

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

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

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

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