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arXiv · 1802.05111

Bounds for twists of $\rm GL(3)$ $L$-functions

Yongxiao Lin
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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 $\varepsilon>0$, 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.

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Yongxiao Lin. 2018-02-14. Bounds for twists of $\rm GL(3)$ $L$-functions. https://arxiv.org/abs/1802.05111

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