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

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