Hybrid bounds for twists of $GL(3)$ $L$-functions

Abstract

Let $\pi$ be a Hecke-Maass cusp form for $SL(3,\mathbb{Z})$ and $\chi ={\chi }_1{\chi }_2$ a Dirichlet character with ${\chi }_i$ primitive modulo $M_i$. Suppose that $M_1$, $M_2$ are primes such that $\max \{(M|t|{)}^{1/3+2\delta /3},M^{2/5}|t{|}^{-9/20},M^{1/2+2\delta }|t{|}^{-3/4+2\delta }\}(M|t|{)}^{\epsilon }<M_1<\min \{(M|t|{)}^{2/5},(M|t|{)}^{1/2-8\delta }\}(M|t|{)}^{-\epsilon }$ for any $\epsilon >0$, where $M=M_1{M}_2$, $|t|\ge 1$ and $0<\delta <1/52$. Then we have $$L\left(\frac{1}{2}+it,\pi \otimes \chi \right){\ll }_{\pi ,\epsilon }(M|t|{)}^{3/4-\delta +\epsilon }.$$

arXiv comment26 pages. Comments are welcome!

References in corpus (1)

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

Cited by in corpus (1)

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