{"paper":{"title":"Subconvex equidistribution of cusp forms: reduction to Eisenstein observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul D. Nelson","submitted_at":"2017-02-09T17:26:38Z","abstract_excerpt":"Let $\\pi$ traverse a sequence of cuspidal automorphic representations of GL(2) with large prime level, unramified central character and bounded infinity type. For G either of the groups GL(1) or PGL(2), let H(G) denote the assertion that subconvexity holds for G-twists of the adjoint $L$-function of $\\pi$, with polynomial dependence upon the conductor of the twist. We show that H(GL(1)) implies H(PGL(2)).\n  In geometric terms, H(PGL(2)) corresponds roughly to an instance of arithmetic quantum unique ergodicity with a power savings in the error term, H(GL(1)) to the special case in which the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02908","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":""},"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"}