Duke Mathematical Journal

Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems

Pavel M. Bleher

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Article information

Source
Duke Math. J., Volume 70, Number 3 (1993), 655-682.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077290892

Digital Object Identifier
doi:10.1215/S0012-7094-93-07015-9

Mathematical Reviews number (MathSciNet)
MR1224102

Zentralblatt MATH identifier
0803.11052

Subjects
Primary: 11P21: Lattice points in specified regions
Secondary: 35P20: Asymptotic distribution of eigenvalues and eigenfunctions 58G18 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 62E20: Asymptotic distribution theory

Citation

Bleher, Pavel M. Distribution of the error term in the Weyl asymptotics for the Laplace operator on a two-dimensional torus and related lattice problems. Duke Math. J. 70 (1993), no. 3, 655--682. doi:10.1215/S0012-7094-93-07015-9. https://projecteuclid.org/euclid.dmj/1077290892


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References

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  • [BCDL] P. M. Bleher, Z. Cheng, F. J. Dyson, and J. L. Lebowitz, Distribution of the error term for the number of lattice points inside a shifted circle, preprint IASSNS-HEP-92/10, Institute for advanced Study, Princeton, 1992.
  • [CdV1] Y. Colin de Verdière, Nombre de points entiers dans une famille homothétique de domains de $\bf R$, Ann. Sci. École Norm. Sup. (4) 10 (1977), no. 4, 559–575.
  • [CdV2] Y. Colin de Verdière, Quasi-modes sur les variétés Riemanniennes, Invent. Math. 43 (1977), no. 1, 15–52.
  • [CL] Z. Cheng and L. J. Lebowitz, Statistics of energy levels in integrable quantum systems, Phys. Rev. A 44 (1991), R3399–R3402.
  • [H-B] D. R. Heath-Brown, The distribution and moments of the error term in the Dirichlet divisor problem, preprint, Oxford Univ., to appear in Acta Arith.
  • [K] D. G. Kendall, On the number of lattice points inside a random oval, Quart. J. Math., Oxford Ser. 19 (1948), 1–26.