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Bounds for twists of GL(3) $L$-functions
Journal of the European Mathematical Society ( IF 2.5 ) Pub Date : 2021-02-03 , DOI: 10.4171/jems/1046
Yongxiao Lin 1
Affiliation  

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 $\pi\otimes \chi$. For any given $\varepsilon > 0$, we establish a subconvex bound $L(1/2+it, \pi\otimes \chi)\ll_{\pi, \varepsilon} (M(|t|+1))^{3/4-1/36+\varepsilon}$, uniformly in both the $M$- and $t$-aspects.

中文翻译:

GL(3)$ L $-函数的扭曲界限

假设$ \ pi $是$ \ mathrm {SL}(3,\ mathbb {Z})$的固定的Hecke-Maass尖点形式,而$ \ chi $是原始的Dirichlet字符模$ M $,我们假定是素数。令$ L(s,\ pi \ otimes \ chi)$为与$ \ pi \ otimes \ chi $相关的$ L $函数。对于任何给定的$ \ varepsilon> 0 $,我们建立一个子凸界$ L(1/2 + it,\ pi \ otimes \ chi)\ ll _ {\ pi,\ varepsilon}(M(| t | +1)) ^ {3 / 4-1 / 36 + \ varepsilon} $,在$ M $-和$ t $方面均相同。
更新日期:2021-04-09
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