The Second Moment of ${\mathrm{G}\mathrm{L}}_4\times {\mathrm{G}\mathrm{L}}_2$ $L$-functions at Special Points

In this paper, we provide an alternative proof of Chandee and Li’s result on the second moment of ${\mathrm{G}\mathrm{L}}_4\times {\mathrm{G}\mathrm{L}}_2$ special $L$-values. Our method is conceptually more direct as it neither detects the `Eisenstein–Kloosterman’ cancellation nor uses the Poisson summation.