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
Source: Duke Math. J. Volume 70, Number 3
(1993), 655-682.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077290892
Mathematical Reviews number (MathSciNet): MR1224102
Zentralblatt MATH identifier: 0803.11052
Digital Object Identifier: doi:10.1215/S0012-7094-93-07015-9
References
[B] P. Bleher, On the distribution of the number of lattice points inside a family of convex ovals, Duke Math. J. 67 (1992), no. 3, 461–481.
Mathematical Reviews (MathSciNet): MR93h:11110
Zentralblatt MATH: 0762.11031
Digital Object Identifier: doi:10.1215/S0012-7094-92-06718-4
Project Euclid: euclid.dmj/1077294534
[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.
Mathematical Reviews (MathSciNet): MR1224087
Zentralblatt MATH: 0781.11038
Digital Object Identifier: doi:10.1007/BF02102104
Project Euclid: euclid.cmp/1104253074
[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.
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[CdV2] Y. Colin de Verdière, Quasi-modes sur les variétés Riemanniennes, Invent. Math. 43 (1977), no. 1, 15–52.
Mathematical Reviews (MathSciNet): MR58:18615
Zentralblatt MATH: 0449.53040
Digital Object Identifier: doi:10.1007/BF01390202
[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.
Mathematical Reviews (MathSciNet): MR1159354
[K] D. G. Kendall, On the number of lattice points inside a random oval, Quart. J. Math., Oxford Ser. 19 (1948), 1–26.
Mathematical Reviews (MathSciNet): MR9,570b
Zentralblatt MATH: 0031.11201
Digital Object Identifier: doi:10.1093/qmath/os-19.1.1
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