Duke Mathematical Journal

Lattice points on ellipses

J. Cilleruelo and A. Córdoba

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 76, Number 3 (1994), 741-750.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077287203

Digital Object Identifier
doi:10.1215/S0012-7094-94-07629-1

Mathematical Reviews number (MathSciNet)
MR1309329

Zentralblatt MATH identifier
0822.11069

Subjects
Primary: 11P21: Lattice points in specified regions
Secondary: 11R04: Algebraic numbers; rings of algebraic integers

Citation

Cilleruelo, J.; Córdoba, A. Lattice points on ellipses. Duke Math. J. 76 (1994), no. 3, 741--750. doi:10.1215/S0012-7094-94-07629-1. http://projecteuclid.org/euclid.dmj/1077287203.


Export citation

References

  • [1] J. Cilleruelo and A. Córdoba, Trigonometric polynomials and lattice points, Proc. Amer. Math. Soc. 115 (1992), no. 4, 899–905.
  • [2] J. Cilleruelo and A. Córdoba, $B\sb 2[\infty]$-sequences of square numbers, Acta Arith. 61 (1992), no. 3, 265–270.
  • [3] J. Cilleruelo and A. Córdoba, La Teoria de los Números, Mondadori, Madrid, 1992.
  • [4] J. Cilleruelo, Arcs containing no three lattice points, Acta Arith. 59 (1991), no. 1, 87–90.
  • [5] J. Cilleruelo, The distribution of the lattice points on circles, J. Number Theory 43 (1993), no. 2, 198–202.
  • [6] J. Cilleruelo, $B_2$-sequences whose terms are squares, preprint.
  • [7] A. Córdoba, Translation invariant operators, Fourier analysis (Proc. Sem., El Escorial, 1979), Asoc. Mat. Espa nola, vol. 1, Asoc. Mat. Espa nola, Madrid, 1980, pp. 117–176.
  • [8] Y. Meyer, Algebraic numbers and harmonic analysis, North-Holland Publishing Co., Amsterdam, 1972.
  • [9] W. Narkiewicz, Elementary and analytic theory of algebraic numbers, PWN—Polish Scientific Publishers, Warsaw, 1974.
  • [10] W. Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203–227.
  • [11] A. Zygmund, A Cantor-Lebesgue theorem for double trigonometric series, Studia Math. 43 (1972), 173–178.
  • [12] A. Zygmund, On Fourier coefficients and transforms of functions of two variables, Studia Math. 50 (1974), 189–201.