The Whittaker period formula on metaplectic 𝑆𝐿₂

Qiu, Yannan

doi:10.1090/tran/7258

The Whittaker period formula on metaplectic $\mathrm {SL}_2$
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Trans. Amer. Math. Soc. 371 (2019), 1083-1117 Request permission

Abstract:

The Whittaker period formula on $\widetilde {\mathrm {SL}}_2(\mathbb {A}_F)$ was previously established only when the base field $F$ is totally real. We present a new simple proof that works for all base number fields. Our local argument is uniform at every local place of $F$, based on the isometry property of quadratic Fourier transform and the estimates of matrix coefficients and Whittaker functions imposed by the unitarity of the local representations.

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