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arXiv · 1702.08271

An explicit inversion formula for the $p$-adic Whittaker transform on $\text{GL}_n(\mathbb{Q}_p)$

João Guerreiro
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Abstract

Whittaker functions on non-archimedean fields were first introduced in the work of Jacquet, and they were characterized explicitly by Shintani. We obtain an explicit inversion formula and a Plancherel formula for the $p$-adic Whittaker transform on $\text{GL}_n(\mathbb{Q}_p)$. As an application, integral representations are obtained for the local factors of certain symmetric power $L$-functions.

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João Guerreiro. 2017-02-27. An explicit inversion formula for the $p$-adic Whittaker transform on $\text{GL}_n(\mathbb{Q}_p)$. https://arxiv.org/abs/1702.08271

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