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arxiv: 1604.08000 · v1 · pith:5O2OVXTCnew · submitted 2016-04-27 · 🧮 math.NT

Twists of GL(3) L-functions

classification 🧮 math.NT
keywords alignfunctionsaddressedassumebeginboundboundscharacter
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Let $\pi$ be a $SL(3,\mathbb Z)$ Hecke-Maass cusp form, and let $\chi$ be a primitive Dirichlet character modulo $M$, which we assume to be prime. In this note we revisit the subconvexity problem addressed in `The circle method and bounds for $L$-functions IV' and establish the following unconditional bound \begin{align*} L\left(\tfrac{1}{2},\pi\otimes\chi\right)\ll M^{3/4-1/308+\varepsilon}. \end{align*}

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  1. A connection between low-lying zeros and central values of $L$-functions

    math.NT 2026-05 unverdicted novelty 6.0

    Partial results on low-lying zero densities imply explicit conditional lower bounds on central L-values, with bound quality tied to family symmetry type and allowed Fourier support.