On the subconvexity problem for $GL(3)\times GL(2)$ $L$ -functions

preprint2011arXivOpen access

Fix $g$ a self-dual Hecke-Maass form for $SL_3(\mathbb{Z})$ . Let $f$ be a holomorphic newform of prime level $q$ and fixed weight. Conditional on a lower bound for a short sum of squares of Fourier coefficients of $f$ , we prove a subconvexity bound in the $q$ aspect for $L(s, g\times f)$ at the central point.

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On the subconvexity problem for $GL(3)\times GL(2)$ $L$ -functions

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On the subconvexity problem for GL(3)×GL(2)GL(3)\times GL(2)GL(3)×GL(2) LLL-functions

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On the subconvexity problem for $GL(3)\times GL(2)$ $L$ -functions