{"paper":{"title":"Spectral Moment Formulae for $\\hbox{GL}(3)\\times \\hbox{GL}(2)$ $\\hbox{L}$-functions II: The Eisenstein Case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Chung-Hang Kwan","submitted_at":"2023-10-13T21:50:50Z","abstract_excerpt":"This work is the second in a series, following Part I (Algebra Number Theory 18.10 (2024)) and preceding Part III (Math. Ann. 391.1 (2025)). We continue our investigation of spectral moments of $\\hbox{GL}(3)\\times \\hbox{GL}(2)$ $\\hbox{L}$-functions from the perspective of period integrals. Using an identity between two distinct periods for the $\\hbox{GL}(3)$ Eisenstein series, we establish an exact Motohashi-type identity linking the shifted cubic moment of $\\hbox{GL}(2)$ $\\hbox{L}$-functions to the shifted fourth moment of $\\hbox{GL}(1)$ $\\hbox{L}$-functions. In addition, we offer a novel, in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.09419","kind":"arxiv","version":3},"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/2310.09419/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"}