We include several results providing bounds for an interval on the hyperbola containing lattice points.
On montre plusieurs résultats à propos de la longueur minimale d’un arc de l’hyperbole contenant points entiers.
@article{JTNB_2000__12_1_87_0,
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},
zbl = {1006.11055},
mrnumber = {1827840},
language = {en},
url = {https://jtnb.centre-mersenne.org/item/JTNB_2000__12_1_87_0/}
}
TY - JOUR AU - Javier Cilleruelo AU - Jorge Jiménez-Urroz 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 - https://jtnb.centre-mersenne.org/item/JTNB_2000__12_1_87_0/ LA - en ID - JTNB_2000__12_1_87_0 ER -
Javier Cilleruelo; Jorge Jiménez-Urroz. The hyperbola $xy = N$. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 1, pp. 87-92. https://jtnb.centre-mersenne.org/item/JTNB_2000__12_1_87_0/
[1] , , Trigonometric polynomials and lattice points. Proc. Amer. Math. Soc. 115 (1992), 899-905. | Zbl | MR
[2] , , Divisors in a Dedekind domain. Acta. Arith. 85 (1998), 229-233. | Zbl | MR
[3] , , The least common multiple and lattice points on hyperbolas. To appear in Quart. J. Math. | Zbl | MR
[4] , , Introduction to the theory of numbers. Clarendon Press. 4th ed., Oxford, 1960. | Zbl | MR