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In particular, we prove $$ \\lambda_F(n)= \\Omega(n^{k-1}\\text{exp} (c \\frac{\\sqrt{\\log n}}{\\log\\log n})), $$ when $c>0$ is an absolute constant. This improves the earlier result $$ \\lambda_F(n)= \\Omega(n^{k-1} (\\frac{\\sqrt{\\log n}}{\\log\\log n})) $$ of Das and the third author. We also show that for any $n \\ge 3$, one has $$ \\lambda_F(n) \\leq n^{k-1}\\text{exp} \\left(c"},"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":"1801.05380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-01-16T17:32:44Z","cross_cats_sorted":[],"title_canon_sha256":"0269013ad3c69ab75c4c373bd94ee628ff699513fa4d348c3dbeb2f32c9702a7","abstract_canon_sha256":"7ca502a0d9002e53767f00b7bcc4dd30181d9d10aeb205ce14a794a8a86316fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:46.933836Z","signature_b64":"fK6+Lv7IhPOVoDmI4TYrIOaSz01zQ/nfqVLBHhM9yOr8JxM6ipAunU9AaT+swDVDQTq+NWFZbfK5JJPRyrp8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d9a9231cfb6442737e98ed0a6c32974a8863687bbb12f442fc026cf6d002401","last_reissued_at":"2026-05-18T00:25:46.933146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:46.933146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Hecke eigenvalues of Siegel modular forms in the Maass space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Biplab Paul, Jyoti Sengupta, Sanoli Gun","submitted_at":"2018-01-16T17:32:44Z","abstract_excerpt":"In this article, we prove an omega-result for the Hecke eigenvalues $\\lambda_F(n)$ of Maass forms $F$ which are Hecke eigenforms in the space of Siegel modular forms of weight $k$, genus two for the Siegel modular group $Sp_2(\\Z)$. In particular, we prove $$ \\lambda_F(n)= \\Omega(n^{k-1}\\text{exp} (c \\frac{\\sqrt{\\log n}}{\\log\\log n})), $$ when $c>0$ is an absolute constant. This improves the earlier result $$ \\lambda_F(n)= \\Omega(n^{k-1} (\\frac{\\sqrt{\\log n}}{\\log\\log n})) $$ of Das and the third author. We also show that for any $n \\ge 3$, one has $$ \\lambda_F(n) \\leq n^{k-1}\\text{exp} \\left(c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05380","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":"1801.05380","created_at":"2026-05-18T00:25:46.933256+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.05380v1","created_at":"2026-05-18T00:25:46.933256+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05380","created_at":"2026-05-18T00:25:46.933256+00:00"},{"alias_kind":"pith_short_12","alias_value":"LWNJEMOPWZCC","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LWNJEMOPWZCCON7J","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LWNJEMOP","created_at":"2026-05-18T12:32:37.024351+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/LWNJEMOPWZCCON7JR3IKNQZJOS","json":"https://pith.science/pith/LWNJEMOPWZCCON7JR3IKNQZJOS.json","graph_json":"https://pith.science/api/pith-number/LWNJEMOPWZCCON7JR3IKNQZJOS/graph.json","events_json":"https://pith.science/api/pith-number/LWNJEMOPWZCCON7JR3IKNQZJOS/events.json","paper":"https://pith.science/paper/LWNJEMOP"},"agent_actions":{"view_html":"https://pith.science/pith/LWNJEMOPWZCCON7JR3IKNQZJOS","download_json":"https://pith.science/pith/LWNJEMOPWZCCON7JR3IKNQZJOS.json","view_paper":"https://pith.science/paper/LWNJEMOP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.05380&json=true","fetch_graph":"https://pith.science/api/pith-number/LWNJEMOPWZCCON7JR3IKNQZJOS/graph.json","fetch_events":"https://pith.science/api/pith-number/LWNJEMOPWZCCON7JR3IKNQZJOS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LWNJEMOPWZCCON7JR3IKNQZJOS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LWNJEMOPWZCCON7JR3IKNQZJOS/action/storage_attestation","attest_author":"https://pith.science/pith/LWNJEMOPWZCCON7JR3IKNQZJOS/action/author_attestation","sign_citation":"https://pith.science/pith/LWNJEMOPWZCCON7JR3IKNQZJOS/action/citation_signature","submit_replication":"https://pith.science/pith/LWNJEMOPWZCCON7JR3IKNQZJOS/action/replication_record"}},"created_at":"2026-05-18T00:25:46.933256+00:00","updated_at":"2026-05-18T00:25:46.933256+00:00"}