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

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

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

@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},
     pages = {87--92},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {1},
     year = {2000},
     mrnumber = {1827840},
     zbl = {1006.11055},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_2000__12_1_87_0/}
}
TY  - JOUR
AU  - Cilleruelo, Javier
AU  - Jiménez-Urroz, Jorge
TI  - The hyperbola $xy = N$
JO  - Journal de théorie des nombres de Bordeaux
PY  - 2000
SP  - 87
EP  - 92
VL  - 12
IS  - 1
PB  - Université Bordeaux I
UR  - http://archive.numdam.org/item/JTNB_2000__12_1_87_0/
LA  - en
ID  - JTNB_2000__12_1_87_0
ER  - 
%0 Journal Article
%A Cilleruelo, Javier
%A Jiménez-Urroz, Jorge
%T The hyperbola $xy = N$
%J Journal de théorie des nombres de Bordeaux
%D 2000
%P 87-92
%V 12
%N 1
%I Université Bordeaux I
%U http://archive.numdam.org/item/JTNB_2000__12_1_87_0/
%G en
%F JTNB_2000__12_1_87_0
Cilleruelo, Javier; Jiménez-Urroz, Jorge. The hyperbola $xy = N$. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 1, pp. 87-92. http://archive.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 | 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