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Small Gaps in the Spectrum of Tori: Asymptotic Formulae

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Abstract

We establish an asymptotic formula, uniformly down to the Planck scale, for the number of small gaps between the first N eigenvalues of the Laplacian on almost all flat tori and also on almost all rectangular flat tori.

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Acknowledgements

We would like to thank the referee for a very careful reading of the manuscript.

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Authors and Affiliations

  1. Mathematisches Institut, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Valentin Blomer

  2. Department of Mathematics, Caltech, 1200 E California Blvd, Pasadena, CA, 91125, USA

    Maksym Radziwiłł

Authors
  1. Valentin Blomer
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  2. Maksym Radziwiłł
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Corresponding author

Correspondence to Maksym Radziwiłł.

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Communicated by S. Dyatlov.

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Valentin Blomer was partially supported by a SNF-DFG lead agency Grants BL 915/2-2 and BL 915/5-1. Maksym Radziwiłł  acknowledges support of a Sloan Fellowship and NSF Grant DMS-1902063.

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Blomer, V., Radziwiłł, M. Small Gaps in the Spectrum of Tori: Asymptotic Formulae. Commun. Math. Phys. 403, 155–180 (2023). https://doi.org/10.1007/s00220-023-04760-3

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  • DOI: https://doi.org/10.1007/s00220-023-04760-3

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