{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4CCIEZ4RFHAITXMJQMNWXOVPAX","short_pith_number":"pith:4CCIEZ4R","schema_version":"1.0","canonical_sha256":"e08482679129c089dd89831b6bbaaf05f5cd957139511ece5f1adefbef9de58d","source":{"kind":"arxiv","id":"1712.00363","version":1},"attestation_state":"computed","paper":{"title":"Subconvexity Bound for Hecke character $L$-Functions of Imaginary quadratic Number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Keshav Aggarwal","submitted_at":"2017-11-30T14:04:14Z","abstract_excerpt":"Let $K=\\mathbb{Q}(\\sqrt{-D})$ be an imaginary number field, $(p)=\\mathfrak{p}\\mathfrak{p}'$ be a split odd prime and $\\psi$ be a Hecke character of conductor $\\mathfrak{p}$. Let $L(s,\\psi)$ be the associated $L$-function. We prove the Burgess bound in $t$-aspect and a hybrid bound in conductor aspect, \\begin{equation*} L(1/2+it,\\psi)\\ll_{D,\\varepsilon} (1+|t|)^{3/8+\\varepsilon}p^{1/8} \\end{equation*} for $p\\ll t$. In Appendix A, we present the ideas for an elementary proof of Voronoi summation formula for holomorphic cusp forms with CM and squarefree level. This is done by exploiting the latti"},"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":"1712.00363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-30T14:04:14Z","cross_cats_sorted":[],"title_canon_sha256":"a4c35b7613c1e09ebdfffb213d4c2686632bf032cb2db3265d53fa97448c14a0","abstract_canon_sha256":"0c00e415338f7764aaf4b60b56617d739aee319772948773e8c95f3959008268"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:06.433648Z","signature_b64":"OjFNN83rDCspboQ/cAmJRJTRIYofJzhHXILs/Uih/ODbGRes6s5XXa0Qz50AtYthExU3MfvaSmqv8VvfleCOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e08482679129c089dd89831b6bbaaf05f5cd957139511ece5f1adefbef9de58d","last_reissued_at":"2026-05-18T00:29:06.432971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:06.432971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subconvexity Bound for Hecke character $L$-Functions of Imaginary quadratic Number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Keshav Aggarwal","submitted_at":"2017-11-30T14:04:14Z","abstract_excerpt":"Let $K=\\mathbb{Q}(\\sqrt{-D})$ be an imaginary number field, $(p)=\\mathfrak{p}\\mathfrak{p}'$ be a split odd prime and $\\psi$ be a Hecke character of conductor $\\mathfrak{p}$. Let $L(s,\\psi)$ be the associated $L$-function. We prove the Burgess bound in $t$-aspect and a hybrid bound in conductor aspect, \\begin{equation*} L(1/2+it,\\psi)\\ll_{D,\\varepsilon} (1+|t|)^{3/8+\\varepsilon}p^{1/8} \\end{equation*} for $p\\ll t$. In Appendix A, we present the ideas for an elementary proof of Voronoi summation formula for holomorphic cusp forms with CM and squarefree level. 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