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September 2019 Loxodromic Eisenstein series for cofinite Kleinian groups
Yosuke Irie
Funct. Approx. Comment. Math. 61(1): 121-137 (September 2019). DOI: 10.7169/facm/1781

Abstract

We introduce an Eisenstein series associated to a loxodromic element of cofinite Kleinian groups, namely the loxodromic Eisenstein series, and study its fundamental properties. It is the analogue of the hyperbolic Eisenstein series for Fuchsian groups of the first kind. We prove the convergence and the differential equation associated to the Laplace-Beltrami operator. We also prove the precise spectral expansion associated to the Laplace-Beltrami operator. Furthermore, we derive the analytic continuation with the location of the possible poles and their residues from the spectral expansion.

Citation

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Yosuke Irie. "Loxodromic Eisenstein series for cofinite Kleinian groups." Funct. Approx. Comment. Math. 61 (1) 121 - 137, September 2019. https://doi.org/10.7169/facm/1781

Information

Published: September 2019
First available in Project Euclid: 29 November 2018

zbMATH: 07126914
MathSciNet: MR4012366
Digital Object Identifier: 10.7169/facm/1781

Subjects:
Primary: 11M36

Rights: Copyright © 2019 Adam Mickiewicz University

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Vol.61 • No. 1 • September 2019
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