{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SNCVPEEGY6SUOEPALC5FCC4NKN","short_pith_number":"pith:SNCVPEEG","schema_version":"1.0","canonical_sha256":"9345579086c7a54711e058ba510b8d537d214c5f686c967be0e45242795a8388","source":{"kind":"arxiv","id":"1708.03003","version":4},"attestation_state":"computed","paper":{"title":"Uniform bounds for sums of Kloosterman sums of half integral weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Dunn","submitted_at":"2017-08-09T20:29:28Z","abstract_excerpt":"For $m,n>0$ and $mn<0$ we estimate the sums \\begin{equation*} \\sum_{c \\leq x} \\frac{S(m,n,c,\\chi)}{c}, \\end{equation*} where the $S(m,n,c,\\chi)$ are Kloosterman sums attached to a multiplier $\\chi$ of weight $1/2$ on the full modular group. Our estimates are uniform in $m, n$ and $x$ in analogy with the bounds for the case $mn<0$ due to Ahlgren-Andersen, and those of Sarnak-Tsimerman for the trivial multiplier when $m,n>0$. In the case $mn<0$, our estimates are stronger in the $mn$-aspect than those of Ahlgren-Andersen. We also obtain a refinement whose quality depends on the factorization of "},"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":"1708.03003","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-08-09T20:29:28Z","cross_cats_sorted":[],"title_canon_sha256":"2fb13094ba82d862aefbbcc830199df361e8404b4e5c0105086462d6a8912690","abstract_canon_sha256":"2f8e6b75a18fe0c2a9fb29e399577cb00bbd741f5e0271585b9202134944d9a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:37.278196Z","signature_b64":"aRXv8v9iXTgs9YcZu+1QcpttCdAe8dzMqVDZCMfN2jJJFxckJIutVhZGv1FNwv+cBU/YAZNz0zzAGqfnYPD8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9345579086c7a54711e058ba510b8d537d214c5f686c967be0e45242795a8388","last_reissued_at":"2026-05-18T00:03:37.277605Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:37.277605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform bounds for sums of Kloosterman sums of half integral weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexander Dunn","submitted_at":"2017-08-09T20:29:28Z","abstract_excerpt":"For $m,n>0$ and $mn<0$ we estimate the sums \\begin{equation*} \\sum_{c \\leq x} \\frac{S(m,n,c,\\chi)}{c}, \\end{equation*} where the $S(m,n,c,\\chi)$ are Kloosterman sums attached to a multiplier $\\chi$ of weight $1/2$ on the full modular group. Our estimates are uniform in $m, n$ and $x$ in analogy with the bounds for the case $mn<0$ due to Ahlgren-Andersen, and those of Sarnak-Tsimerman for the trivial multiplier when $m,n>0$. In the case $mn<0$, our estimates are stronger in the $mn$-aspect than those of Ahlgren-Andersen. We also obtain a refinement whose quality depends on the factorization of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03003","kind":"arxiv","version":4},"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":"1708.03003","created_at":"2026-05-18T00:03:37.277682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.03003v4","created_at":"2026-05-18T00:03:37.277682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03003","created_at":"2026-05-18T00:03:37.277682+00:00"},{"alias_kind":"pith_short_12","alias_value":"SNCVPEEGY6SU","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SNCVPEEGY6SUOEPA","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SNCVPEEG","created_at":"2026-05-18T12:31:43.269735+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/SNCVPEEGY6SUOEPALC5FCC4NKN","json":"https://pith.science/pith/SNCVPEEGY6SUOEPALC5FCC4NKN.json","graph_json":"https://pith.science/api/pith-number/SNCVPEEGY6SUOEPALC5FCC4NKN/graph.json","events_json":"https://pith.science/api/pith-number/SNCVPEEGY6SUOEPALC5FCC4NKN/events.json","paper":"https://pith.science/paper/SNCVPEEG"},"agent_actions":{"view_html":"https://pith.science/pith/SNCVPEEGY6SUOEPALC5FCC4NKN","download_json":"https://pith.science/pith/SNCVPEEGY6SUOEPALC5FCC4NKN.json","view_paper":"https://pith.science/paper/SNCVPEEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.03003&json=true","fetch_graph":"https://pith.science/api/pith-number/SNCVPEEGY6SUOEPALC5FCC4NKN/graph.json","fetch_events":"https://pith.science/api/pith-number/SNCVPEEGY6SUOEPALC5FCC4NKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SNCVPEEGY6SUOEPALC5FCC4NKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SNCVPEEGY6SUOEPALC5FCC4NKN/action/storage_attestation","attest_author":"https://pith.science/pith/SNCVPEEGY6SUOEPALC5FCC4NKN/action/author_attestation","sign_citation":"https://pith.science/pith/SNCVPEEGY6SUOEPALC5FCC4NKN/action/citation_signature","submit_replication":"https://pith.science/pith/SNCVPEEGY6SUOEPALC5FCC4NKN/action/replication_record"}},"created_at":"2026-05-18T00:03:37.277682+00:00","updated_at":"2026-05-18T00:03:37.277682+00:00"}