{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:R4GELHJSC7Y6OKMVL34CUJ55SG","short_pith_number":"pith:R4GELHJS","canonical_record":{"source":{"id":"1707.04814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-16T03:20:43Z","cross_cats_sorted":[],"title_canon_sha256":"039e319ad5fb89ab2f611860eff913d4757af6871c0524907eed2bd6c9f6e9c2","abstract_canon_sha256":"ef4e5b9afcea7262851c4e759695aadf5a4cbf977f215332344a21923adf9a45"},"schema_version":"1.0"},"canonical_sha256":"8f0c459d3217f1e729955ef82a27bd91a25ec9c0cab78ce8f2a61b4a5b3521b0","source":{"kind":"arxiv","id":"1707.04814","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04814","created_at":"2026-05-18T00:40:12Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04814v1","created_at":"2026-05-18T00:40:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04814","created_at":"2026-05-18T00:40:12Z"},{"alias_kind":"pith_short_12","alias_value":"R4GELHJSC7Y6","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R4GELHJSC7Y6OKMV","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R4GELHJS","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:R4GELHJSC7Y6OKMVL34CUJ55SG","target":"record","payload":{"canonical_record":{"source":{"id":"1707.04814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-16T03:20:43Z","cross_cats_sorted":[],"title_canon_sha256":"039e319ad5fb89ab2f611860eff913d4757af6871c0524907eed2bd6c9f6e9c2","abstract_canon_sha256":"ef4e5b9afcea7262851c4e759695aadf5a4cbf977f215332344a21923adf9a45"},"schema_version":"1.0"},"canonical_sha256":"8f0c459d3217f1e729955ef82a27bd91a25ec9c0cab78ce8f2a61b4a5b3521b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:12.140148Z","signature_b64":"0t8fKOKLfAX02/86GAxpC0LLqZz4l9QPgOxOJxT3ndGObQQfrMUgnH6MAlcvNnsGcjo/EHtvHOTIPkOk6q3sDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f0c459d3217f1e729955ef82a27bd91a25ec9c0cab78ce8f2a61b4a5b3521b0","last_reissued_at":"2026-05-18T00:40:12.139533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:12.139533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.04814","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WTgRrhLE7fc9faK4yg3YxbeBTpURzD6yIqUKT5LBsi7bpSNynyXE3aoLcmd6rgc2wVwvF5F1mlq3RpUDz9KZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:45:12.722450Z"},"content_sha256":"96eab6f2c994a9c9be7535f95f1229d1c46d6858062f7c304bf5002d1cafa859","schema_version":"1.0","event_id":"sha256:96eab6f2c994a9c9be7535f95f1229d1c46d6858062f7c304bf5002d1cafa859"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:R4GELHJSC7Y6OKMVL34CUJ55SG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Period polynomials, derivatives of $L$-functions, and zeros of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Larry Rolen, Nikolaos Diamantis","submitted_at":"2017-07-16T03:20:43Z","abstract_excerpt":"Period polynomials have long been fruitful tools for the study of values of $L$-functions in the context of major outstanding conjectures. In this paper, we survey some facets of this study from the perspective of Eichler cohomology. We discuss ways to incorporate non-cuspidal modular forms and values of derivatives of $L$-functions into the same framework. We further review investigations of the location of zeros of the period polynomial as well as of its analogue for $L$-derivatives."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04814","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a6Ym9oQODRshZuYEQZ15s+ypHLiNRWNXwxb2uQGM4a6id+ED/EVz2hDDQbS9fXNSYCIqRJJoyan9K4esYXGfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T09:45:12.722981Z"},"content_sha256":"78968508fb953091c8bb6a6af3f5490f89d0a6208081941a9ff63d05be7db078","schema_version":"1.0","event_id":"sha256:78968508fb953091c8bb6a6af3f5490f89d0a6208081941a9ff63d05be7db078"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4GELHJSC7Y6OKMVL34CUJ55SG/bundle.json","state_url":"https://pith.science/pith/R4GELHJSC7Y6OKMVL34CUJ55SG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4GELHJSC7Y6OKMVL34CUJ55SG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T09:45:12Z","links":{"resolver":"https://pith.science/pith/R4GELHJSC7Y6OKMVL34CUJ55SG","bundle":"https://pith.science/pith/R4GELHJSC7Y6OKMVL34CUJ55SG/bundle.json","state":"https://pith.science/pith/R4GELHJSC7Y6OKMVL34CUJ55SG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4GELHJSC7Y6OKMVL34CUJ55SG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R4GELHJSC7Y6OKMVL34CUJ55SG","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":"ef4e5b9afcea7262851c4e759695aadf5a4cbf977f215332344a21923adf9a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-16T03:20:43Z","title_canon_sha256":"039e319ad5fb89ab2f611860eff913d4757af6871c0524907eed2bd6c9f6e9c2"},"schema_version":"1.0","source":{"id":"1707.04814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04814","created_at":"2026-05-18T00:40:12Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04814v1","created_at":"2026-05-18T00:40:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04814","created_at":"2026-05-18T00:40:12Z"},{"alias_kind":"pith_short_12","alias_value":"R4GELHJSC7Y6","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R4GELHJSC7Y6OKMV","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R4GELHJS","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:78968508fb953091c8bb6a6af3f5490f89d0a6208081941a9ff63d05be7db078","target":"graph","created_at":"2026-05-18T00:40:12Z","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":"Period polynomials have long been fruitful tools for the study of values of $L$-functions in the context of major outstanding conjectures. In this paper, we survey some facets of this study from the perspective of Eichler cohomology. We discuss ways to incorporate non-cuspidal modular forms and values of derivatives of $L$-functions into the same framework. We further review investigations of the location of zeros of the period polynomial as well as of its analogue for $L$-derivatives.","authors_text":"Larry Rolen, Nikolaos Diamantis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-16T03:20:43Z","title":"Period polynomials, derivatives of $L$-functions, and zeros of polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04814","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":"sha256:96eab6f2c994a9c9be7535f95f1229d1c46d6858062f7c304bf5002d1cafa859","target":"record","created_at":"2026-05-18T00:40:12Z","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":"ef4e5b9afcea7262851c4e759695aadf5a4cbf977f215332344a21923adf9a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-16T03:20:43Z","title_canon_sha256":"039e319ad5fb89ab2f611860eff913d4757af6871c0524907eed2bd6c9f6e9c2"},"schema_version":"1.0","source":{"id":"1707.04814","kind":"arxiv","version":1}},"canonical_sha256":"8f0c459d3217f1e729955ef82a27bd91a25ec9c0cab78ce8f2a61b4a5b3521b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f0c459d3217f1e729955ef82a27bd91a25ec9c0cab78ce8f2a61b4a5b3521b0","first_computed_at":"2026-05-18T00:40:12.139533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:12.139533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0t8fKOKLfAX02/86GAxpC0LLqZz4l9QPgOxOJxT3ndGObQQfrMUgnH6MAlcvNnsGcjo/EHtvHOTIPkOk6q3sDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:12.140148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.04814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96eab6f2c994a9c9be7535f95f1229d1c46d6858062f7c304bf5002d1cafa859","sha256:78968508fb953091c8bb6a6af3f5490f89d0a6208081941a9ff63d05be7db078"],"state_sha256":"5569e95a6946353322bafd18287e0cc7c8430e4bdfe183f6fbd3bed25f09a5e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4FyxYFXxKhyKzrLVNJN/z029BwumGQNLmsycUDmu/s/yocZFeHQ76JlW5si2eCJ4HMnPEmgdg8NntWGOqjyuAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T09:45:12.725554Z","bundle_sha256":"2433714148d2b50a8f707ca912142eb1f0d4a6e061bc9bbde78fc21e081f494f"}}