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arXiv · 1311.6120

The circle method and bounds for $L$-functions - IV: Subconvexity for twists of $GL(3)$ $L$-functions - B

Ritabrata Munshi
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Abstract

Let $π$ be a $SL(3,\mathbb Z)$ Hecke-Maass cusp form satisfying the Ramanujan conjecture and the Selberg-Ramanujan conjecture, and let $χ$ be a primitive Dirichlet character modulo $M$, which we assume to be prime for simplicity. We will prove the following subconvex bound $$ L\left(\tfrac{1}{2},π\otimesχ\right)\ll_{π,\varepsilon} M^{\frac{3}{4}-\frac{1}{1612}+\varepsilon}. $$

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Ritabrata Munshi. 2014-02-16. The circle method and bounds for $L$-functions - IV: Subconvexity for twists of $GL(3)$ $L$-functions - B. https://arxiv.org/abs/1311.6120

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