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In this paper we shall consider the sum: \\[ S:= \\frac{1}{H}\\sum_{h\\leq H} V\\left( \\frac{h}{H}\\right)\\sum_{n\\leq N} \\lambda_1 (n) \\lambda_2 (n+h) \\lambda_3 (n+ 2h)W\\left( \\frac{n}{N} \\right), \\] \\noindent where $V$ and $W$ are smooth bump functions, supported on $[1, 2]$. We shall prove a nontrivial upper bound, under the assumption that $H\\geq N^{1/2+ \\epsilon}$."},"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":"1608.07063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-25T09:37:18Z","cross_cats_sorted":[],"title_canon_sha256":"882b822505add6a690a85cf1dbf172a7f4fac253bc526c0f7a388651bc43d5f6","abstract_canon_sha256":"cb869bd3f81499a0b018c2c4b9144950cb0ed463be5b2be4408d6c3ad401e814"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:54.905432Z","signature_b64":"2qX/fgozPX3SqI+yZpZT3xQF7QHb9wNBEjB3nbPkQDjQEhtQAO+kt5c2spQuwPdoi5evCoIaDj1a2mLQLIdNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d388ef34842c0aa1fd21f1a34606142061bb626d0668b3afc3b3002ec0a7c36a","last_reissued_at":"2026-05-18T01:07:54.905041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:54.905041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On double shifted convolution sum of $SL(2, \\mathbb{Z})$ Hecke eigen forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Saurabh Kumar Singh","submitted_at":"2016-08-25T09:37:18Z","abstract_excerpt":"Let $\\lambda_i (n)$ $i= 1, 2, 3$ denote the normalised Fourier coefficients of holomorphic eigenform or Maass cusp form. In this paper we shall consider the sum: \\[ S:= \\frac{1}{H}\\sum_{h\\leq H} V\\left( \\frac{h}{H}\\right)\\sum_{n\\leq N} \\lambda_1 (n) \\lambda_2 (n+h) \\lambda_3 (n+ 2h)W\\left( \\frac{n}{N} \\right), \\] \\noindent where $V$ and $W$ are smooth bump functions, supported on $[1, 2]$. We shall prove a nontrivial upper bound, under the assumption that $H\\geq N^{1/2+ \\epsilon}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07063","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.07063","created_at":"2026-05-18T01:07:54.905097+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.07063v1","created_at":"2026-05-18T01:07:54.905097+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07063","created_at":"2026-05-18T01:07:54.905097+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OEO6NEEFQFK","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OEO6NEEFQFKD7JB","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OEO6NEE","created_at":"2026-05-18T12:29:55.572404+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/2OEO6NEEFQFKD7JB6GRUMBQUEB","json":"https://pith.science/pith/2OEO6NEEFQFKD7JB6GRUMBQUEB.json","graph_json":"https://pith.science/api/pith-number/2OEO6NEEFQFKD7JB6GRUMBQUEB/graph.json","events_json":"https://pith.science/api/pith-number/2OEO6NEEFQFKD7JB6GRUMBQUEB/events.json","paper":"https://pith.science/paper/2OEO6NEE"},"agent_actions":{"view_html":"https://pith.science/pith/2OEO6NEEFQFKD7JB6GRUMBQUEB","download_json":"https://pith.science/pith/2OEO6NEEFQFKD7JB6GRUMBQUEB.json","view_paper":"https://pith.science/paper/2OEO6NEE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.07063&json=true","fetch_graph":"https://pith.science/api/pith-number/2OEO6NEEFQFKD7JB6GRUMBQUEB/graph.json","fetch_events":"https://pith.science/api/pith-number/2OEO6NEEFQFKD7JB6GRUMBQUEB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OEO6NEEFQFKD7JB6GRUMBQUEB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OEO6NEEFQFKD7JB6GRUMBQUEB/action/storage_attestation","attest_author":"https://pith.science/pith/2OEO6NEEFQFKD7JB6GRUMBQUEB/action/author_attestation","sign_citation":"https://pith.science/pith/2OEO6NEEFQFKD7JB6GRUMBQUEB/action/citation_signature","submit_replication":"https://pith.science/pith/2OEO6NEEFQFKD7JB6GRUMBQUEB/action/replication_record"}},"created_at":"2026-05-18T01:07:54.905097+00:00","updated_at":"2026-05-18T01:07:54.905097+00:00"}