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The remainder in Weyl's law for random two-dimensional

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Abstract.

We prove that the average order of the remainder in counting the number of points of a random lattice inside a disc of radius \( \sqrt{\lambda} \) \( {\cal O}(\lambda^{1/4+\epsilon}) \). Our proof is spectral in nature.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, Montreal, Canada, e-mail: petridis@math.mcgill.ca, , , , , , CA

    Y. Petridis

  2. Department of Mathematics and Statistics, McGill University, Montreal, Canada, e-mail: jtoth@math.mcgill.ca, , , , , , CA

    J.A. Toth

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  1. Y. Petridis
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  2. J.A. Toth
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Submitted: July 2001, Revised: August 2001, Revised: March 2002.

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Petridis, Y., Toth, J. The remainder in Weyl's law for random two-dimensional . GAFA, Geom. funct. anal. 12, 756–775 (2002). https://doi.org/10.1007/s00039-002-8265-5

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  • DOI: https://doi.org/10.1007/s00039-002-8265-5

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