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The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces

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Toeplitz Centennial

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 4))

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Abstract

The counting numbers for discrete subgroups of motions in Euclidean and non-Euclidean spaces are found using the wave equation as the principal tool. In 2 and 3 dimensions the error estimates are close to the best known.

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References

  1. Hardy, G.H.: On Dirichlet’s divisor problem, Proc. London Math. Soc. (2) vol. 15 (1916) 1–25.

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  2. Hua, Loo-Keng: The lattice points in a circle, Quart. Jr. Math., Oxford Series, vol. 13 (1942) 18–29.

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  5. Patterson, S.J.: A lattice point problem in hyperbolic space, Mathematika, vol. 22 (1975) 81–88.

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Author information

Authors and Affiliations

  1. Courant Institute, New York University, 251 Mercer Street, New York, N.Y., 10012, USA

    Peter D. Lax

  2. Department of Mathematics, Stanford University, Stanford, California, 94305, USA

    Ralph S. Phillips

Authors
  1. Peter D. Lax
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  2. Ralph S. Phillips
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Israel

    I. Gohberg

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© 1982 Springer Basel AG

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Lax, P.D., Phillips, R.S. (1982). The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces. In: Gohberg, I. (eds) Toeplitz Centennial. Operator Theory: Advances and Applications, vol 4. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5183-1_22

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  • DOI: https://doi.org/10.1007/978-3-0348-5183-1_22

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5184-8

  • Online ISBN: 978-3-0348-5183-1

  • eBook Packages: Springer Book Archive

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