论文标题
$ \ mathrm {sl}（2）（2）\ times \ mathrm {gl}（2）$
The unramified computation of a Shimura integral for $\mathrm{SL}(2)\times \mathrm{GL}(2)$
论文作者
论文摘要
在本说明中，我们重新访问Shimura类型的Rankin-Selberg积分，以供$ \ Mathrm {Sl} _2 \ Times \ Times \ Mathrm {Gl} _2 $的通用表示形式，由Ginzburg，Rallis和Soudry构建。我们给出了不同的``固有''证明未受到的计算的证明。与他们的证明相反，我们避免了通用线性组的本地功能方程，但使用Casselman-Shalika公式用于未受到的Whittaker函数，用于$ \ Mathrm {SL} _2 $和$ \ MATHRM {GL} _2 _2 $。
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 $\mathrm{GL}_2$.
