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Mixed moment and joint non-vanishing of $\mathrm{GL}(3)\times\mathrm{GL}(1)$ and $\mathrm{GL}(1)$ $L$-functions
In this article, we study the mixed-moment problem for the product of central values of two $L$-functions twisted by a Dirichlet character of large conductor $q$. Precisely, for a fixed $\mathrm{SL}_3(\mathbb{Z})$ Hecke-Maass cusp form $π$, we asymptotically evaluate the first moment, with $\textit{
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