Weyl bound for trilinear periods via conformal bootstrap

2025/08/28 by Anshul Adve, James Bonifacio, Adve, Anshul +11 · 1 citation
Mathematics · #Analytic Number Theory Research #Mathematical Dynamics and Fractals #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2508.20576

Abstract

Let f₁,f₂ be holomorphic modular forms of the same weight for a cocompact lattice Γ< PSL₂(R). We estimate the rate of decay of the coefficients in the expansion of f₁f₂ 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.

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