Automorphic ${\mathrm{SL}}_2$-periods and the subconvexity problem for ${\mathrm{GL}}_2\times {\mathrm{GL}}_3$

Abstract

We prove a new (conditional) result towards the subconvexity problem for certain automorphic $L$-functions for ${\mathrm{GL}}_2\times {\mathrm{GL}}_3$. This follows from the computation of new ${\mathrm{SL}}_2$-period integrals associated with newforms $f$ and $g$ of even weight and odd squarefree level. The same computations also lead to a central value formula for degree $6$ complex $L$-series of the form $L(f\otimes \mathrm{Ad}(g),s)$, extending previous work in arXiv:1804.02352.

31 pages; minor corrections from previous version; to appear in Mathematika