Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions in the level aspect

Zhiwei Liu

In this paper, we establish an asymptotic formula of mixed moments of $L(1/2,f)$ and $L(1/2,{\mathrm{sym}}^{2}f)$ for cusp forms $f$ of weight $k$, prime level $q$ and real primitive…