Hybrid subconvexity bounds for twisted $L$-functions on $GL(3)$

Abstract

Let $q$ be a large prime, and $\chi$ the quadratic character modulo $q$. Let $\varphi$ be a self-dual Hecke--Maass cusp form for $SL(3,\mathbb{Z})$, and $u_j$ a Hecke--Maass cusp form for ${\Gamma }_0(q)\subseteq SL(2,\mathbb{Z})$ with spectral parameter $t_j$. We prove the hybrid subconvexity bounds for the twisted $L$-functions \[ L(1/2,ϕ\times u_j\timesχ)\ll_{ϕ,\varepsilon} (qt_j)^{3/2-θ+\varepsilon},\quad L(1/2+it,ϕ\timesχ)\ll_{ϕ,\varepsilon} (qt)^{3/4-θ/2+\varepsilon}, \] for any $\epsilon >0$, where $\theta =1/23$ is admissible.

35 pages. Comments are welcome! Accepted for publication in Sci China Math

References in corpus (1)

• Bounds for twisted symmetric square $L$-functions - III

Cited by in corpus (5)

• Bounds for twists of $\mathrm{GL}(3)$ $L$-functions
• Subconvexity for $\mathrm{GL}(3)$ L-functions
• Hybrid bounds for twists of $GL(3)$ $L$-functions
• Subconvexity for $L$-Functions on ${\mathrm{GL}}_3$ over Number Fields
• Subconvexity for twisted $L$-functions on ${\mathrm{GL}}_3$ over the Gaussian number field