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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.02908","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-09T17:26:38Z","cross_cats_sorted":[],"title_canon_sha256":"7c73bec52950516be644f7fa6022961d9226a5eaf4e6e9862a0e9f708d91a7d6","abstract_canon_sha256":"0ebc59a3c5662ee6f37d4054f5fc5fb4d25bea1bc19fddc6d433219f385bb3c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:36.810944Z","signature_b64":"rZ0GjIE+Pzuc8YpZ/+kR0ie6AK6wT0pIg/bbaGALSyhwyyc+gsgV5ZUREXMv9+rRSk5ayJE6SGcqqCkmFG0RDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bed954c455476c0882f3dc08eada8458f0bb8a5c4264711720a84e2f763e180a","last_reissued_at":"2026-05-17T23:40:36.810528Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:36.810528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.02908","created_at":"2026-05-17T23:40:36.810598+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.02908v3","created_at":"2026-05-17T23:40:36.810598+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02908","created_at":"2026-05-17T23:40:36.810598+00:00"},{"alias_kind":"pith_short_12","alias_value":"X3MVJRCVI5WA","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"X3MVJRCVI5WARAXT","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"X3MVJRCV","created_at":"2026-05-18T12:31:53.515858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X3MVJRCVI5WARAXT3QEOVWUELD","json":"https://pith.science/pith/X3MVJRCVI5WARAXT3QEOVWUELD.json","graph_json":"https://pith.science/api/pith-number/X3MVJRCVI5WARAXT3QEOVWUELD/graph.json","events_json":"https://pith.science/api/pith-number/X3MVJRCVI5WARAXT3QEOVWUELD/events.json","paper":"https://pith.science/paper/X3MVJRCV"},"agent_actions":{"view_html":"https://pith.science/pith/X3MVJRCVI5WARAXT3QEOVWUELD","download_json":"https://pith.science/pith/X3MVJRCVI5WARAXT3QEOVWUELD.json","view_paper":"https://pith.science/paper/X3MVJRCV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.02908&json=true","fetch_graph":"https://pith.science/api/pith-number/X3MVJRCVI5WARAXT3QEOVWUELD/graph.json","fetch_events":"https://pith.science/api/pith-number/X3MVJRCVI5WARAXT3QEOVWUELD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X3MVJRCVI5WARAXT3QEOVWUELD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X3MVJRCVI5WARAXT3QEOVWUELD/action/storage_attestation","attest_author":"https://pith.science/pith/X3MVJRCVI5WARAXT3QEOVWUELD/action/author_attestation","sign_citation":"https://pith.science/pith/X3MVJRCVI5WARAXT3QEOVWUELD/action/citation_signature","submit_replication":"https://pith.science/pith/X3MVJRCVI5WARAXT3QEOVWUELD/action/replication_record"}},"created_at":"2026-05-17T23:40:36.810598+00:00","updated_at":"2026-05-17T23:40:36.810598+00:00"}