Hybrid subconvexity bounds for $L\left(\frac{1}{2},{\text{Sym}}^{2}f\otimes g\right)$

Abstract

Fix an integer $\kappa ⩾2$. Let $P$ be prime and let $k>\kappa$ be an even integer. For $f$ a holomorphic cusp form of weight $k$ and full level and $g$ a primitive holomorphic cusp form of weight $2\kappa$ and level $P$, we prove hybrid subconvexity bounds for $L\left(\frac{1}{2},{\text{Sym}}^{2}f\otimes g\right)$ in the $k$ and $P$ aspects when $P^{\frac{13}{64}+\delta }<k<P^{\frac{3}{8}-\delta }$ for any $0<\delta <\frac{11}{128}$. These bounds are achieved through a first moment method (with amplification when $P^{\frac{13}{64}}<k⩽P^{\frac{4}{13}}$).

1st draft, 27 pages

References in corpus (2)

• Distribution of mass of holomorphic cusp forms
• The circle method and bounds for $L$-functions - II: Subconvexity for twists of GL(3) $L$-functions