The hyperbola xy=N
Journal de théorie des nombres de Bordeaux, Volume 12 (2000) no. 1, p. 87-92

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

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

@article{JTNB_2000__12_1_87_0,
     author = {Cilleruelo, Javier and Jim\'enez-Urroz, Jorge},
     title = {The hyperbola $xy = N$},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {1},
     year = {2000},
     pages = {87-92},
     zbl = {1006.11055},
     mrnumber = {1827840},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2000__12_1_87_0}
}
Cilleruelo, Javier; Jiménez-Urroz, Jorge. The hyperbola $xy = N$. Journal de théorie des nombres de Bordeaux, Volume 12 (2000) no. 1, pp. 87-92. http://www.numdam.org/item/JTNB_2000__12_1_87_0/

[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