# Level Aspect Subconvexity For Rankin-Selberg $L$-functions

@inproceedings{Holowinsky2012LevelAS, title={Level Aspect Subconvexity For Rankin-Selberg \$L\$-functions}, author={Roman Holowinsky and Ritabrata Munshi}, year={2012} }

Let $M$ be a square-free integer and let $P$ be a prime not dividing $M$ such that $P \sim M^\eta$ with $0<\eta<2/21$. We prove subconvexity bounds for $L(\tfrac{1}{2}, f \otimes g)$ when $f$ and $g$ are two primitive holomorphic cusp forms of levels $P$ and $M$. These bounds are achieved through an unamplified second moment method.

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## Sub-convexity problem for Rankin-Selberg $L$-functions

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## Hybrid subconvexity bounds for $L \left(\tfrac{1}{2}, \text{Sym}^2 f \otimes g\right)$

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## First moment of Rankin–Selberg central L-values and subconvexity in the level aspect

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