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arXiv · 2210.13653

The unramified computation of a Shimura integral for $\mathrm{SL}(2)\times \mathrm{GL}(2)$

Pan Yan
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Abstract

In this note, we revisit the Rankin-Selberg integral of Shimura type for generic representations of $\mathrm{SL}_2\times \mathrm{GL}_2$, constructed by Ginzburg, Rallis, and Soudry. We give a different and more ``intrinsic'' proof of the unramified computation. In contrast to their proof we avoid local functional equation for the general linear groups but use the Casselman-Shalika formulas for unramified Whittaker functions for $\mathrm{SL}_2$ and $\mathrm{GL}_2$.

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BibTeXRIS

Pan Yan. 2022-10-24. The unramified computation of a Shimura integral for $\mathrm{SL}(2)\times \mathrm{GL}(2)$. https://doi.org/10.1216/rmj.2023.53.1313

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