Geometric Counting on Wavefront Real Spherical Spaces

Bernhard Krötz; Eitan Sayag; Henrik Schlichtkrull

doi:10.1007/s10114-017-7164-5

Geometric Counting on Wavefront Real Spherical Spaces

Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	488-531
Number of pages	44
Journal	Acta Mathematica Sinica, English Series
Volume	34
Issue number	3
DOIs	https://doi.org/10.1007/s10114-017-7164-5
State	Published - 1 Mar 2018

Keywords

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

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s10114-017-7164-5

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title = "Geometric Counting on Wavefront Real Spherical Spaces",

abstract = "We provide Lp-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, error term, lattice counting, norm comparison of eigenfunctions, real spherical spaces, spectral analysis, wavefront lemma",

author = "Bernhard Kr{\"o}tz and Eitan Sayag and Henrik Schlichtkrull",

note = "Publisher Copyright: {\textcopyright} 2018, 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.",

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AU - Krötz, Bernhard

AU - Sayag, Eitan

AU - Schlichtkrull, Henrik

N1 - Publisher Copyright: © 2018, 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.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - We provide Lp-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.

AB - We provide Lp-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.

KW - Homogeneous spaces

KW - error term

KW - lattice counting

KW - norm comparison of eigenfunctions

KW - real spherical spaces

KW - spectral analysis

KW - wavefront lemma

UR - https://www.scopus.com/pages/publications/85037718794

U2 - 10.1007/s10114-017-7164-5

DO - 10.1007/s10114-017-7164-5

M3 - Article

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JF - Acta Mathematica Sinica, English Series

IS - 3

ER -

Geometric Counting on Wavefront Real Spherical Spaces

Abstract

Keywords

ASJC Scopus subject areas

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