A spectral identity for second moments of Eisenstein series of O(n, 1)

João Pedro Boavida

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arXiv · 1502.00881

A spectral identity for second moments of Eisenstein series of O(n, 1)

João Pedro Boavida

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Abstract

Let H=O(n)xO(1) be an anisotropic subgroup of G=O(n, 1) and let A be the adele ring of k=Q. Consider the periods of an Eisenstein series 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 the Eisenstein series.

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João Pedro Boavida. 2015-02-03. A spectral identity for second moments of Eisenstein series of O(n, 1). https://arxiv.org/abs/1502.00881

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