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Three Applications of the Siegel Mass Formula

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Geometric Aspects of Functional Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2256))

Abstract

We present three applications of the Siegel mass formula, using the explicit upper bounds for densities derived in Bourgain and Demeter (Int Math Res Not 2015(11):3150–3184, 2014).

The authors are partially supported by the Collaborative Research NSF grant DMS-1800305.

AMS Subject Classification Primary 11L03

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References

  1. J. Bourgain, C. Demeter, New bounds for the discrete Fourier restriction to the sphere in 4D and 5D. Int. Math. Res. Not. 2015(11), 3150–3184 (2014)

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  2. J. Bourgain, C. Demeter, Mean value estimates for Weyl sums in two dimensions. J. Lond. Math. Soc. (2) 94(3), 814–838 (2016)

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  3. J. Bourgain, Z. Rudnick, P. Sarnak, Spatial statistics for lattice points on the sphere I: individual results. Bull. Iranian Math. Soc. 43(4), 361–386 (2017)

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  5. Y. Kitaoka, Arithmetic of Quadratic Forms. Cambridge Tracts in Mathematics, vol. 106 (Cambridge University Press, Cambridge, 1993)

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  6. L.C. Siegel, Lectures on the Analytical Theory of Quadratic Forms: Second Term 1934–1935 The Institute for Advanced Study and Princeton University, Revised edition 1949, Reprinted January 1955

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Author information

Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Princeton, NJ, USA

    Jean Bourgain

  2. Department of Mathematics, Indiana University, Bloomington, IN, USA

    Ciprian Demeter

Authors
  1. Jean Bourgain
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  2. Ciprian Demeter
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Corresponding author

Correspondence to Ciprian Demeter .

Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel, Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel

    Bo'az Klartag

  2. Department of Mathematics, Technion – Israel Institute of Technology, Haifa, Israel

    Emanuel Milman

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Bourgain, J., Demeter, C. (2020). Three Applications of the Siegel Mass Formula. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2256. Springer, Cham. https://doi.org/10.1007/978-3-030-36020-7_6

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