Hybrid bounds for twists of $GL(3)$ $L$-functions
Hybrid bounds for twists of $GL(3)$ $L$-functions
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DOI：
10.5565/publmat6412003
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发表时间：
2017-05
期刊：
影响因子：
--
通讯作者：
Qingfeng Sun
中科院分区：
文献类型：
--
作者：
Qingfeng Sun
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 $\max\{(M|t|)^{1/3+2\delta/3},M^{2/5}|t|^{-9/20}, M^{1/2+2\delta}|t|^{-3/4+2\delta}\}(M|t|)^{\varepsilon} 0$, where $M=M_1M_2$, $|t|\geq 1$ and $0<\delta< 1/52$. Then we have $$ L\left(\frac{1}{2}+it,\pi\otimes \chi\right)\ll_{\pi,\varepsilon} (M|t|)^{3/4-\delta+\varepsilon}. $$
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 $\max\{(M|t|)^{1/3+2\delta/3},M^{2/5}|t|^{-9/20}, M^{1/2+2\delta}|t|^{-3/4+2\delta}\}(M|t|)^{\varepsilon} 0$, where $M=M_1M_2$, $|t|\geq 1$ and $0<\delta< 1/52$. Then we have $$ L\left(\frac{1}{2}+it,\pi\otimes \chi\right)\ll_{\pi,\varepsilon} (M|t|)^{3/4-\delta+\varepsilon}. $$