{"paper":{"title":"Weyl bound for trilinear periods via conformal bootstrap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.NT","authors_text":"Alex Radcliffe, Anshul Adve, Dalimil Mazac, Gordon Rogelberg, James Bonifacio, Petr Kravchuk, Sridip Pal","submitted_at":"2025-08-28T09:13:54Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20576","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.20576/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}