The hyperbola x y = N

Javier Cilleruelo; Jorge Jiménez-Urroz

Journal de théorie des nombres de Bordeaux (2000)

  • Volume: 12, Issue: 1, page 87-92
  • ISSN: 1246-7405

Abstract

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

How to cite

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Cilleruelo, Javier, and Jiménez-Urroz, Jorge. "The hyperbola $xy = N$." Journal de théorie des nombres de Bordeaux 12.1 (2000): 87-92. <http://eudml.org/doc/248511>.

@article{Cilleruelo2000,
abstract = {We include several results providing bounds for an interval on the hyperbola $xy = N$ containing $k$ lattice points.},
author = {Cilleruelo, Javier, Jiménez-Urroz, Jorge},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {asymptotic results; divisor function; lattice points on hyperbolas},
language = {eng},
number = {1},
pages = {87-92},
publisher = {Université Bordeaux I},
title = {The hyperbola $xy = N$},
url = {http://eudml.org/doc/248511},
volume = {12},
year = {2000},
}

TY - JOUR
AU - Cilleruelo, Javier
AU - Jiménez-Urroz, Jorge
TI - The hyperbola $xy = N$
JO - Journal de théorie des nombres de Bordeaux
PY - 2000
PB - Université Bordeaux I
VL - 12
IS - 1
SP - 87
EP - 92
AB - We include several results providing bounds for an interval on the hyperbola $xy = N$ containing $k$ lattice points.
LA - eng
KW - asymptotic results; divisor function; lattice points on hyperbolas
UR - http://eudml.org/doc/248511
ER -

References

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  1. [1] J. Cilleruelo, A. Córdoba, Trigonometric polynomials and lattice points. Proc. Amer. Math. Soc.115 (1992), 899-905. Zbl0777.11035MR1089403
  2. [2] J. Cilleruelo, J. Jiménez-Urroz, Divisors in a Dedekind domain. Acta. Arith.85 (1998), 229-233. Zbl0910.11043MR1627827
  3. [3] A. Granville, J. Jiménez-Urroz, The least common multiple and lattice points on hyperbolas. To appear in Quart. J. Math. Zbl0983.11058MR1782098
  4. [4] G.H. Hardy, E.M. Wright, Introduction to the theory of numbers. Clarendon Press. 4th ed., Oxford, 1960. Zbl0086.25803MR568909

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