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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.20576 |
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Table of Contents:
- Let $f_1,f_2$ be holomorphic modular forms of the same weight for a cocompact lattice $Γ< \mathrm{PSL}_2(\mathbf{R})$. 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 $Γ$ 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.