Bounds for twists of $\mathrm{GL}(3)$ $L$-functions

Abstract

Let $\pi$ be a fixed Hecke--Maass cusp form for $\mathrm{SL}(3,\mathbb{Z})$ and $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be a prime. Let $L(s,\pi \otimes \chi )$ be the $L$-function associated to $\pi \otimes \chi$. In this paper, for any given $\epsilon >0$, we establish a subconvex bound $L(1/2+it,\pi \otimes \chi ){\ll }_{\pi ,\epsilon }(M(|t|+1){)}^{3/4-1/36+\epsilon }$, uniformly in both the $M$- and $t$-aspects.

arXiv comment19 pages; to appear in JEMS

References in corpus (9)

• The subconvexity problem for $\GL_{2}$
• Distribution of mass of holomorphic cusp forms
• Oscillatory integrals with uniformity in parameters
• On the subconvexity problem for L-functions on GL(3)
• Subconvexity for symmetric square $L$-functions
• Hybrid subconvexity bounds for twisted $L$-functions on $GL(3)$
• Subconvexity for $\mathrm{GL}(3)$ L-functions
• Subconvexity for L-functions of non-spherical cusp forms on GL(3)
• Hybrid bounds for twists of $GL(3)$ $L$-functions

Cited by in corpus (4)

• The Burgess bound via a trivial delta method
• Algebraic twists of ${\mathrm{GL}}_3\times {\mathrm{GL}}_2$ $L$-functions
• A new subconvex bound for $\mathrm{GL}(3)$ $L$-functions in the $t$-aspect
• Subconvexity for twisted $L$-functions on ${\mathrm{GL}}_3$ over the Gaussian number field