{"paper":{"title":"Uniform subconvexity bounds for $GL(2)\\times GL(2)$ $L$-functions in the spectral aspect","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Zhao Xu","submitted_at":"2025-09-07T08:18:58Z","abstract_excerpt":"In this paper, we study the second moment for $GL(2)\\times GL(2)$ $L$-functions $L(\\frac{1}{2},f\\times g)$, which leads to a uniform subconvexity bound in the spectral aspect. In particular, if either $f$ or $g$ is a dihedral Maass newform, or if one of them has level $1$, we obtain a Burgess-type bound that is uniform in both $t_f$ and $t_g$, where $t_f$, $t_g$ denote the spectral parameters of $f$, $g$. As an application, we also establish a shrinking result for QUE in the case of dihedral Maass newforms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05968","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/2509.05968/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"}