{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JAHPLBOYFR7MWOI2744MFQZCIV","short_pith_number":"pith:JAHPLBOY","canonical_record":{"source":{"id":"1703.07944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-23T06:20:11Z","cross_cats_sorted":[],"title_canon_sha256":"6a50b82fbeca021d3f0f6db68db9efe8b8c872dca9db029f701a6034d95ae762","abstract_canon_sha256":"96d016b21ff71afe79c9ddf1159ab4633ae636793e1d2212cab3fc8bb73dcf55"},"schema_version":"1.0"},"canonical_sha256":"480ef585d82c7ecb391aff38c2c322457d6fe4632afaaba25fdbbf4a093499e2","source":{"kind":"arxiv","id":"1703.07944","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07944","created_at":"2026-05-18T00:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07944v1","created_at":"2026-05-18T00:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07944","created_at":"2026-05-18T00:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"JAHPLBOYFR7M","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"JAHPLBOYFR7MWOI2","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"JAHPLBOY","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JAHPLBOYFR7MWOI2744MFQZCIV","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-23T06:20:11Z","cross_cats_sorted":[],"title_canon_sha256":"6a50b82fbeca021d3f0f6db68db9efe8b8c872dca9db029f701a6034d95ae762","abstract_canon_sha256":"96d016b21ff71afe79c9ddf1159ab4633ae636793e1d2212cab3fc8bb73dcf55"},"schema_version":"1.0"},"canonical_sha256":"480ef585d82c7ecb391aff38c2c322457d6fe4632afaaba25fdbbf4a093499e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:04.317682Z","signature_b64":"aVgzhK/t6IvKcBhi1RJOKXpB+oTUnHRxE4EieHJzBsDq3vXFOg4Qg1wNVpHB0l6KP52ibh0kGTTvV6gMIf65Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"480ef585d82c7ecb391aff38c2c322457d6fe4632afaaba25fdbbf4a093499e2","last_reissued_at":"2026-05-18T00:48:04.316985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:04.316985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07944","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":"2026-05-18T00:48:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9eCG7bqOpoYuSRexLmzJ/fIhyH/mYogrZMCmvIMm84nTJOdAcgOeoSHAQy79m/7Tdhn3xgPN2Ymdj4WpwzpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:36:24.501240Z"},"content_sha256":"ae8ff09340f9bd2aea8e917b0170077f4b3d371e52958878f8887a7114458627","schema_version":"1.0","event_id":"sha256:ae8ff09340f9bd2aea8e917b0170077f4b3d371e52958878f8887a7114458627"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JAHPLBOYFR7MWOI2744MFQZCIV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effective joint distribution of eigenvalues of Hecke operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sudhir Pujahari","submitted_at":"2017-03-23T06:20:11Z","abstract_excerpt":"In 1997, Serre proved that the eigenvalues of normalised $p$-th Hecke operator $T^{'}_p$ acting on the space of cusp forms of weight $k$ and level $N$ are equidistributed in $[-2,2]$ with respect to a measure that converge to the Sato-Tate measure, whenever $N+k \\to \\infty$. In 2009, Murty and Sinha proved the effective version of Serre's theorem. In 2011, using Kuznetsov trace formula, Lau and Wang derived the effective joint distribution of eigenvalues of normalized Hecke operators acting on the space of primitive cusp forms of weight $k$ and level $1$. In this paper, we extend the result of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07944","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":"2026-05-18T00:48:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QO6rSGIfHzsrtuvywGH3WrkcSIAPh7dNMpCc60xKHXv2b1tsPQp+WRuuKVG+YHvrtNGBvRfGKEyp5q2lkXo3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:36:24.501855Z"},"content_sha256":"4e85d353c2981d8a6da9a2b3149e373dd5056ee3d20b6c9ac63f78b0860879c3","schema_version":"1.0","event_id":"sha256:4e85d353c2981d8a6da9a2b3149e373dd5056ee3d20b6c9ac63f78b0860879c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JAHPLBOYFR7MWOI2744MFQZCIV/bundle.json","state_url":"https://pith.science/pith/JAHPLBOYFR7MWOI2744MFQZCIV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JAHPLBOYFR7MWOI2744MFQZCIV/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":"2026-05-26T20:36:24Z","links":{"resolver":"https://pith.science/pith/JAHPLBOYFR7MWOI2744MFQZCIV","bundle":"https://pith.science/pith/JAHPLBOYFR7MWOI2744MFQZCIV/bundle.json","state":"https://pith.science/pith/JAHPLBOYFR7MWOI2744MFQZCIV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JAHPLBOYFR7MWOI2744MFQZCIV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JAHPLBOYFR7MWOI2744MFQZCIV","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":"96d016b21ff71afe79c9ddf1159ab4633ae636793e1d2212cab3fc8bb73dcf55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-23T06:20:11Z","title_canon_sha256":"6a50b82fbeca021d3f0f6db68db9efe8b8c872dca9db029f701a6034d95ae762"},"schema_version":"1.0","source":{"id":"1703.07944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07944","created_at":"2026-05-18T00:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07944v1","created_at":"2026-05-18T00:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07944","created_at":"2026-05-18T00:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"JAHPLBOYFR7M","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"JAHPLBOYFR7MWOI2","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"JAHPLBOY","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:4e85d353c2981d8a6da9a2b3149e373dd5056ee3d20b6c9ac63f78b0860879c3","target":"graph","created_at":"2026-05-18T00:48:04Z","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":"In 1997, Serre proved that the eigenvalues of normalised $p$-th Hecke operator $T^{'}_p$ acting on the space of cusp forms of weight $k$ and level $N$ are equidistributed in $[-2,2]$ with respect to a measure that converge to the Sato-Tate measure, whenever $N+k \\to \\infty$. In 2009, Murty and Sinha proved the effective version of Serre's theorem. In 2011, using Kuznetsov trace formula, Lau and Wang derived the effective joint distribution of eigenvalues of normalized Hecke operators acting on the space of primitive cusp forms of weight $k$ and level $1$. In this paper, we extend the result of","authors_text":"Sudhir Pujahari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-23T06:20:11Z","title":"Effective joint distribution of eigenvalues of Hecke operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07944","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:ae8ff09340f9bd2aea8e917b0170077f4b3d371e52958878f8887a7114458627","target":"record","created_at":"2026-05-18T00:48:04Z","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":"96d016b21ff71afe79c9ddf1159ab4633ae636793e1d2212cab3fc8bb73dcf55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-23T06:20:11Z","title_canon_sha256":"6a50b82fbeca021d3f0f6db68db9efe8b8c872dca9db029f701a6034d95ae762"},"schema_version":"1.0","source":{"id":"1703.07944","kind":"arxiv","version":1}},"canonical_sha256":"480ef585d82c7ecb391aff38c2c322457d6fe4632afaaba25fdbbf4a093499e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"480ef585d82c7ecb391aff38c2c322457d6fe4632afaaba25fdbbf4a093499e2","first_computed_at":"2026-05-18T00:48:04.316985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:04.316985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aVgzhK/t6IvKcBhi1RJOKXpB+oTUnHRxE4EieHJzBsDq3vXFOg4Qg1wNVpHB0l6KP52ibh0kGTTvV6gMIf65Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:04.317682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae8ff09340f9bd2aea8e917b0170077f4b3d371e52958878f8887a7114458627","sha256:4e85d353c2981d8a6da9a2b3149e373dd5056ee3d20b6c9ac63f78b0860879c3"],"state_sha256":"0cedd9e2096e0c26644cbb054924ed03676d324fa0c04ed85b0c9663218e65a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IW+Mic2h9PO36wM/QDnpa0ohJYDZDfBzFhTJgHcuSSvwwnLB/URpc7fia+XcDWJh7YVO7diHEXlNWHanVMFFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:36:24.505517Z","bundle_sha256":"f3a74ee9dcb4b02f7de27fc65dc1790194c3f8cbcace222e5e4f9da7322eb181"}}