{"paper":{"title":"Large sieves for $\\mathrm{GL}_n$ and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Pascadi, Jesse Thorner","submitted_at":"2025-08-20T17:56:58Z","abstract_excerpt":"Let $\\mathfrak{F}_n$ be the set of unitary cuspidal automorphic representations of $\\mathrm{GL}_n$ over a number field $F$, and let $S\\subseteq\\mathfrak{F}_n$ be an arbitrary finite subset. Given $\\pi_0\\in\\mathfrak{F}_{n_0}$, we establish large sieve inequalities for the families $\\{L(s,\\pi)\\colon \\pi\\in S\\}$ and $\\{L(s,\\pi\\times\\pi_0)\\colon \\pi\\in S\\}$ that, unlike previous results, are independent of progress towards the generalized Ramanujan conjecture, and simultaneously handle the Dirichlet coefficients of $L$, $L^{-1}$, and $\\log L$. We also give the first such result that improves upon "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.14888","kind":"arxiv","version":2},"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/2508.14888/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"}