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The Weyl bound for triple product L-functions
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abstract
Let $\pi_1, \pi_2, \pi_3$ be three cuspidal automorphic representations for the group ${\rm SL}(2, \Bbb{Z})$, where $\pi_1$ and $\pi_2$ are fixed and $\pi_3$ has large conductor. We prove a subconvex bound for $L(1/2, \pi_1 \otimes \pi_2 \otimes \pi_3)$ of Weyl-type quality. Allowing $\pi_3$ to be an Eisenstein series we also obtain a Weyl-type subconvex bound for $L(1/2 + it, \pi_1 \otimes \pi_2)$.
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Spectral Reciprocity for the first moment of triple product $L$-functions and applications
A twisted first moment of triple product L-functions satisfies a spectral reciprocity formula, yielding a level-aspect subconvexity bound with saving 225/2624 unconditionally.
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