{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SMLZ4DYOQJX5266RJ25F6AH3L2","short_pith_number":"pith:SMLZ4DYO","schema_version":"1.0","canonical_sha256":"93179e0f0e826fdd7bd14eba5f00fb5ebed5c5b10a0cedd27e8ed409a6bcde73","source":{"kind":"arxiv","id":"2511.08445","version":2},"attestation_state":"computed","paper":{"title":"Non-abelian amplification and bilinear forms with Kloosterman sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Pascadi","submitted_at":"2025-11-11T16:47:34Z","abstract_excerpt":"We introduce a new method to bound bilinear (Type II) sums of Kloosterman sums with composite moduli $c$, using Fourier analysis on $\\mathrm{SL}_2(\\mathbb{Z}/c\\mathbb{Z})$ and an amplification argument with non-abelian characters. For sums of length $\\sqrt{c}$, our method produces a non-trivial bound for all moduli except near-primes, saving $c^{-1/12}$ for products of two primes of the same size. Combining this with previous results for prime moduli, we achieve savings beyond the P\\'olya-Vinogradov range for all moduli. We give applications to moments of twisted cuspidal $L$-functions, and to"},"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":"2511.08445","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-11-11T16:47:34Z","cross_cats_sorted":[],"title_canon_sha256":"9288bc22a200d7141e769cb0e6c61d6dcb29acb5014b0ade88f78c1dae4cfca7","abstract_canon_sha256":"db312df7182cca8c2dc19c52da87df95e2ece9fd0a5a04eba6b7d151316c3b0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:18.324430Z","signature_b64":"gnPZBX28uplgwaB6i2Frf53nSPKWV/ybaPkoOaPyiRNvrCBjP7ymYdptwl1ZG9Xo+GStwQDswRiN0zL7wxZ2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93179e0f0e826fdd7bd14eba5f00fb5ebed5c5b10a0cedd27e8ed409a6bcde73","last_reissued_at":"2026-06-23T02:13:18.323963Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:18.323963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-abelian amplification and bilinear forms with Kloosterman sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Pascadi","submitted_at":"2025-11-11T16:47:34Z","abstract_excerpt":"We introduce a new method to bound bilinear (Type II) sums of Kloosterman sums with composite moduli $c$, using Fourier analysis on $\\mathrm{SL}_2(\\mathbb{Z}/c\\mathbb{Z})$ and an amplification argument with non-abelian characters. For sums of length $\\sqrt{c}$, our method produces a non-trivial bound for all moduli except near-primes, saving $c^{-1/12}$ for products of two primes of the same size. Combining this with previous results for prime moduli, we achieve savings beyond the P\\'olya-Vinogradov range for all moduli. We give applications to moments of twisted cuspidal $L$-functions, and to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.08445","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/2511.08445/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2511.08445","created_at":"2026-06-23T02:13:18.324023+00:00"},{"alias_kind":"arxiv_version","alias_value":"2511.08445v2","created_at":"2026-06-23T02:13:18.324023+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.08445","created_at":"2026-06-23T02:13:18.324023+00:00"},{"alias_kind":"pith_short_12","alias_value":"SMLZ4DYOQJX5","created_at":"2026-06-23T02:13:18.324023+00:00"},{"alias_kind":"pith_short_16","alias_value":"SMLZ4DYOQJX5266R","created_at":"2026-06-23T02:13:18.324023+00:00"},{"alias_kind":"pith_short_8","alias_value":"SMLZ4DYO","created_at":"2026-06-23T02:13:18.324023+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/SMLZ4DYOQJX5266RJ25F6AH3L2","json":"https://pith.science/pith/SMLZ4DYOQJX5266RJ25F6AH3L2.json","graph_json":"https://pith.science/api/pith-number/SMLZ4DYOQJX5266RJ25F6AH3L2/graph.json","events_json":"https://pith.science/api/pith-number/SMLZ4DYOQJX5266RJ25F6AH3L2/events.json","paper":"https://pith.science/paper/SMLZ4DYO"},"agent_actions":{"view_html":"https://pith.science/pith/SMLZ4DYOQJX5266RJ25F6AH3L2","download_json":"https://pith.science/pith/SMLZ4DYOQJX5266RJ25F6AH3L2.json","view_paper":"https://pith.science/paper/SMLZ4DYO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2511.08445&json=true","fetch_graph":"https://pith.science/api/pith-number/SMLZ4DYOQJX5266RJ25F6AH3L2/graph.json","fetch_events":"https://pith.science/api/pith-number/SMLZ4DYOQJX5266RJ25F6AH3L2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SMLZ4DYOQJX5266RJ25F6AH3L2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SMLZ4DYOQJX5266RJ25F6AH3L2/action/storage_attestation","attest_author":"https://pith.science/pith/SMLZ4DYOQJX5266RJ25F6AH3L2/action/author_attestation","sign_citation":"https://pith.science/pith/SMLZ4DYOQJX5266RJ25F6AH3L2/action/citation_signature","submit_replication":"https://pith.science/pith/SMLZ4DYOQJX5266RJ25F6AH3L2/action/replication_record"}},"created_at":"2026-06-23T02:13:18.324023+00:00","updated_at":"2026-06-23T02:13:18.324023+00:00"}