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Acta Mathematica Sinica, English Series

, Volume 34, Issue 3, pp 488–531 | Cite as

Geometric Counting on Wavefront Real Spherical Spaces

  • Bernhard Krötz
  • Eitan Sayag
  • Henrik Schlichtkrull
Article
  • 32 Downloads

Abstract

We provide L p -versus L-bounds for eigenfunctions on a real spherical space Z of wavefront type. It is shown that these bounds imply a non-trivial error term estimate for lattice counting on Z. The paper also serves as an introduction to geometric counting on spaces of the mentioned type.

Keywords

Homogeneous spaces real spherical spaces lattice counting error term wavefront lemma spectral analysis norm comparison of eigenfunctions 

MR(2010) Subject Classification

22E40 22E46 43A85 

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Notes

Acknowledgements

We wish to thank the referee for his insistence on technical detail and clarity of arguments. It eventually made this article much more readable.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Bernhard Krötz
    • 1
  • Eitan Sayag
    • 2
  • Henrik Schlichtkrull
    • 3
  1. 1.Institut f¨ur MathematikUniversität PaderbornPaderbornDeutschland
  2. 2.Department of MathematicsBen Gurion University of the NegevBe’er ShevaIsrael
  3. 3.Department of MathematicsUniversity of CopenhagenCopenhagen ØDenmark

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