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Winter 2013 A spectral identity for second moments of Eisenstein series of $\mathrm{O}(n,1)$
João Pedro Boavida
Illinois J. Math. 57(4): 1111-1130 (Winter 2013). DOI: 10.1215/ijm/1417442564

Abstract

Let $H=\mathrm{O}(n)\times\mathrm{O}(1)$ be an anisotropic subgroup of $G=\mathrm{O} (n,1)$ and let $\mathbb{A} $ be the adele ring of $k=\mathbb{Q}$. Consider the periods

\[(E_{\varphi },F)_{H}=\int_{H_{k}\backslash H_\mathbb{A}}E_{\varphi}\cdot{\overline {F}},\]

of an Eisenstein series $E_{\varphi}$ on $G$ against a form $F$ on $H$. Relying on a variant of Levi–Sobolev spaces, we describe certain Poincaré series as fundamental solutions for the Laplacian, and use them to establish a spectral identity concerning the second moments (in $F$-aspect) of $E_{\varphi }$.

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João Pedro Boavida. "A spectral identity for second moments of Eisenstein series of $\mathrm{O}(n,1)$." Illinois J. Math. 57 (4) 1111 - 1130, Winter 2013. https://doi.org/10.1215/ijm/1417442564

Information

Published: Winter 2013
First available in Project Euclid: 1 December 2014

zbMATH: 1302.11031
MathSciNet: MR3285869
Digital Object Identifier: 10.1215/ijm/1417442564

Subjects:
Primary: 11F67
Secondary: 11E45, 11F72, 43A85, 43A90, 46E35

Rights: Copyright © 2013 University of Illinois at Urbana-Champaign

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Vol.57 • No. 4 • Winter 2013
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