Work

Weyl bound for trilinear periods via conformal bootstrap

Year: 2025

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2508.20576

Authors: Adve, Anshul, Bonifacio, James, Kravchuk, Petr, Mazac, Dalimil, Pal, Sridip, Radcliffe, Alex, Rogelberg, Gordon

Institutions: Centre National de la Recherche Scientifique, Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Institut de Physique Théorique

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, Government of the United Kingdom, UK Research and Innovation, King's College London, Office of Science, Walter Burke Institute for Theoretical Physics, HORIZON EUROPE Framework Programme, Science and Technology Facilities Council, High Energy Physics

Awards: G1099677550, Graduate Research Fellowship Program (GRFP), From the Planck Scale to the Hubble Scale - Theoretical Physics At KCL, G5496282665, G7587271361, G8046890258, G9001110046

OpenAlex ID: W4414448985

Cites: 3

Cited by: 4

Related to: 10