A Godement-Jacquet type integral and the metaplectic Shalika model

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.

References in corpus (2)

• Chtoucas de Drinfeld, formule des traces d'Arthur-Selberg et correspondance de Langlands
• A Casselman-Shalika formula for the Shalika model of GL_n

Cited by in corpus (3)

• Doubling Constructions and Tensor Product $L$-Functions: coverings of the symplectic group
• Doubling constructions: Global functoriality for non-generic cuspidal representations
• Doubling Constructions: the complete L-function for coverings of the symplectic group