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

@article{Pal2020AutomorphicA, title={Automorphic \$\mathrm\{SL\}\_2\$-periods and the subconvexity problem for \$\mathrm\{GL\}\_2 \times \mathrm\{GL\}\_3\$}, author={Aprameyo Pal and Carlos de Vera-Piquero}, journal={arXiv: Number Theory}, year={2020} }

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.

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