Abstract
The Whittaker period formula on S L ~ 2 ( A F ) \widetilde {\mathrm {SL}}_2(\mathbb {A}_F) was previously established only when the base field F 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 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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