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arXiv · 1603.01671

A Godement-Jacquet type integral and the metaplectic Shalika model

Eyal Kaplan·Jan Möllers
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Abstract

We present a novel integral representation for a quotient of global automorphic L-functions, the symmetric square over the exterior square. The pole of this integral characterizes a period of a residual representation of an Eisenstein series. As such, the integral itself constitutes a period, of an arithmetic nature. The construction involves the study of local and global aspects of a new model for double covers of general linear groups, the metaplectic Shalika model. In particular, we prove uniqueness results over p-adic and Archimedean fields, and a new Casselman-Shalika type formula.

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Eyal Kaplan, Jan Möllers. 2016-03-05. A Godement-Jacquet type integral and the metaplectic Shalika model. https://doi.org/10.1353/ajm.2019.0005

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