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arXiv · 2508.20576

Weyl bound for trilinear periods via conformal bootstrap

Anshul Adve·James Bonifacio·Petr Kravchuk·Dalimil Mazac·Sridip Pal·Alex Radcliffe·Gordon Rogelberg
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Abstract

Let $f_1,f_2$ be holomorphic modular forms of the same weight for a cocompact lattice $\Gamma < \mathrm{PSL}_2(\mathbf{R})$. We estimate the rate of decay of the coefficients in the expansion of $f_1\overline{f_2}$ in a Laplace eigenbasis. By specializing our main theorem to the case where $\Gamma$ is arithmetic, we obtain new instances of the Weyl bound for triple product $L$-functions in the spectral aspect. Our method builds on the conformal bootstrap in physics.

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Anshul Adve, James Bonifacio, Petr Kravchuk, Dalimil Mazac, Sridip Pal, Alex Radcliffe, Gordon Rogelberg. 2025-08-28. Weyl bound for trilinear periods via conformal bootstrap. https://arxiv.org/abs/2508.20576

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