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Bounds for twists of $\rm GL(3)$ $L$-functions
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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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Cited by 1 Pith paper
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Squarefree numbers in short intervals: explicit and formalized
For intervals of length H = X^{1/5 - 2/90935 + ε}, the number of squarefree integers differs from (6/π²)H by at most an explicit constant times H X^{-ε/10^{25}}.
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