Subconvexity for $GL(3)\times GL(2)$ twists (with an appendix by Will Sawin)

Abstract

Let $\pi$ be a $SL(3,\mathbb{Z})$ Hecke-Maass cusp form, $f$ be a $SL(2,\mathbb{Z})$ holomorphic cusp form or Maass cusp form and $\chi$ be any non-trivial character $\mathrm{mod}p$, where $p$ is prime. We show that the $L$-function associated with this triplet satisfy \begin{equation*} L\left(\frac{1}{2},π\times f\timesχ\right)\ll_{π,f,ε} p^{\frac{3}{2}-\frac{1}{16}+ε}. \end{equation*} The method also yields the subconvex bound \begin{equation*} L\left(\frac{1}{2},π\otimes χ\right)\ll_{π,ε}p^{\frac{3}{4}-\frac{1}{32}+ε}. \end{equation*}

Final version

References in corpus (6)

• On the Rankin--Selberg problem
• Bounds for twisted symmetric square $L$-functions - III
• Algebraic twists of ${\mathrm{GL}}_3\times {\mathrm{GL}}_2$ $L$-functions
• Primes in arithmetic progressions to large moduli I: Fixed residue classes
• Bounds for twisted symmetric square $L$-functions
• New integral representations for Rankin-Selberg L-functions

Cited by in corpus (1)

• Hybrid subconvexity bounds for twists of $\mathrm{GL}(3)\times \mathrm{GL}(2)$ $L$-functions