{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Q76WTZSJSYBNYE5STQVXBNFA2K","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3399171c997b69d91cb0dd9c61fb5b5dd838b479b10f2f9103773fa701b31f2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-04T16:49:16Z","title_canon_sha256":"8f34309b916196c9638a9b23e19f3b4ad92ae65eaa716bfd10f7e2232f02351d"},"schema_version":"1.0","source":{"id":"1203.0749","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.0749","created_at":"2026-05-18T04:00:50Z"},{"alias_kind":"arxiv_version","alias_value":"1203.0749v1","created_at":"2026-05-18T04:00:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.0749","created_at":"2026-05-18T04:00:50Z"},{"alias_kind":"pith_short_12","alias_value":"Q76WTZSJSYBN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q76WTZSJSYBNYE5S","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q76WTZSJ","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:ed3cf9d0c2cdae55fc695529618e52d0cd310db8bf35a18c26280545800da74a","target":"graph","created_at":"2026-05-18T04:00:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $f\\in S_k(N,\\psi)$ be a newform, and let $\\chi$ be a primitive character of conductor $q^{\\ell}$. Assume that $q$ is a prime and $\\ell>1$. In this paper we describe a method to establish convexity breaking bounds of the form $$ L(\\tfrac{1}{2},\\Sym f\\otimes\\chi)\\ll_{f,\\varepsilon} q^{3/4\\ell-\\delta_{\\ell}+\\varepsilon} $$ for some $\\delta_{\\ell}>0$ and any $\\varepsilon>0$. In particular, for $\\ell=3$ we show that the bound holds with $\\delta_{\\ell}=1/4$.","authors_text":"Ritabrata Munshi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-04T16:49:16Z","title":"Bounds for twisted symmetric square $L$-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0749","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bd8acf6e705e3937248f770c02b3c874afa61b66d613278aae9f940a7bf1d23f","target":"record","created_at":"2026-05-18T04:00:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3399171c997b69d91cb0dd9c61fb5b5dd838b479b10f2f9103773fa701b31f2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-04T16:49:16Z","title_canon_sha256":"8f34309b916196c9638a9b23e19f3b4ad92ae65eaa716bfd10f7e2232f02351d"},"schema_version":"1.0","source":{"id":"1203.0749","kind":"arxiv","version":1}},"canonical_sha256":"87fd69e6499602dc13b29c2b70b4a0d28e54014a34eafc8eaad930335345d8c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87fd69e6499602dc13b29c2b70b4a0d28e54014a34eafc8eaad930335345d8c1","first_computed_at":"2026-05-18T04:00:50.633534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:50.633534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QITEAOuvopVIypjNnr7YAReY93jPcIRX3gN07t3ZAD7ZFeNhzXbbdwxJdY9ZThbeflHlwkY6QtjT7wK3Lb85Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:50.634003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.0749","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd8acf6e705e3937248f770c02b3c874afa61b66d613278aae9f940a7bf1d23f","sha256:ed3cf9d0c2cdae55fc695529618e52d0cd310db8bf35a18c26280545800da74a"],"state_sha256":"d24bfdea7a3d74dd4b48ef3dc6fb09c07329550c34cfb624ef00fc3e81b82d51"}