A Converse Theorem for Metaplectic Eisenstein Series on $SL_2(\mathbb{A})$

Vladislav Petkov

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arXiv · 1504.07331

A Converse Theorem for Metaplectic Eisenstein Series on $SL_2(\mathbb{A})$

Vladislav Petkov

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Abstract

The purpose of this work is to produce a converse theorem for adelic Eisenstein series on the double metaplectic cover of the group $SL_2(\mathbb{A})$. We show that the double Dirichlet series, which satisfy the natural functional equations required in our theorem, are in fact Mellin transforms at infinity of metaplectic Eisenstein series.

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Vladislav Petkov. 2015-04-28. A Converse Theorem for Metaplectic Eisenstein Series on $SL_2(\mathbb{A})$. https://arxiv.org/abs/1504.07331

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