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arXiv · 2101.12106

The Weyl bound for triple product L-functions

Valentin Blomer·Subhajit Jana·Paul D. Nelson
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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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Valentin Blomer, Subhajit Jana, Paul D. Nelson. 2021-01-28. The Weyl bound for triple product L-functions. https://doi.org/10.1215/00127094-2022-0058

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