Spectral decomposition of pseudo-cuspforms, and meromorphic continuation of Eisenstein series, on $\mathbb{Q}$-rank one arithmetic quotients

Iver Walkoe

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arXiv · 1911.12838

Spectral decomposition of pseudo-cuspforms, and meromorphic continuation of Eisenstein series, on $\mathbb{Q}$-rank one arithmetic quotients

Iver Walkoe

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Abstract

We extend Lax-Phillips' theorem on discreteness of pseudo-cuspforms, in the style of Colin de Verdi{\`e}re's use of the Friedrichs self-adjoint extension of a restriction of the Laplace-Beltrami operator, as opposed to the use of semigroup methods. We use this to prove meromorphic continuation of Eisenstein series in several $\mathbb{Q}$-rank one cases, again following Colin de Verdi{\`e}re, as opposed to the semigroup-oriented viewpoint of Lax-Phillips and W. Mueller.

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Iver Walkoe. 2019-11-28. Spectral decomposition of pseudo-cuspforms, and meromorphic continuation of Eisenstein series, on $\mathbb{Q}$-rank one arithmetic quotients. https://arxiv.org/abs/1911.12838

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