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December 2021 A quantitative study of orbit counting and discrete spectrum for anti-de Sitter 3-manifolds
Kazuki Kannaka
Proc. Japan Acad. Ser. A Math. Sci. 97(10): 93-97 (December 2021). DOI: 10.3792/pjaa.97.018

Abstract

Let $\Gamma$ be a discontinuous group for the 3-dimensional anti-de Sitter space $\mathrm{AdS}^{3}:=\mathrm{SO}_{0}(2,2)/\mathrm{SO}_{0}(2,1)$. In this article, we discuss a growth rate of the counting of $\Gamma$-orbits at infinity and the discrete spectrum of the hyperbolic Laplacian of the complete anti-de Sitter manifold $\Gamma\backslash\mathrm{AdS}^{3}$.

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Kazuki Kannaka. "A quantitative study of orbit counting and discrete spectrum for anti-de Sitter 3-manifolds." Proc. Japan Acad. Ser. A Math. Sci. 97 (10) 93 - 97, December 2021. https://doi.org/10.3792/pjaa.97.018

Information

Published: December 2021
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.3792/pjaa.97.018

Subjects:
Primary: 22E40
Secondary: 53C50 , 58J50

Keywords: Anti-de Sitter manifold , Anti-de Sitter space , counting problem , discontinuous group , hyperbolic Laplacian

Rights: Copyright © 2021 The Japan Academy

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Vol.97 • No. 10 • December 2021
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