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This article establishes an asymptotic formula with a power-saving error term for the following sum \\begin{equation*}\n  \\sum_{1 \\leqslant m \\leqslant X} \\sum_{1 \\leqslant n\\leqslant Y} A(Q(m,n)), \\end{equation*} where $X>1$ and $Y\\leqslant X$."},"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":"2303.15856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-03-28T09:53:28Z","cross_cats_sorted":[],"title_canon_sha256":"3a1ca427c4415aad6f34122c45df3e9fb655a8bb78de982da80d1c8c37baad46","abstract_canon_sha256":"2205795005e10acade9468b0e9e618a860559e7b1b66946f0b06c91fbf73f683"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:17:42.222951Z","signature_b64":"vzxfDqt2G8r0EQAjPfzfHBzEtKE/AmvU7Bb5gpWQ00+1rg+SEAghUy2Vciq5Ep3u6HFZsh3Nb4Ofbp9CUDwwAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb5c4422a5ccdcbbfd922a30b0c3d408d3060f9d68dfed3d4fee7688d279a9d7","last_reissued_at":"2026-06-25T01:17:42.222425Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:17:42.222425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sum of the $GL(3)$ Fourier coefficients over quadratics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Himanshi Chanana, Saurabh Kumar Singh","submitted_at":"2023-03-28T09:53:28Z","abstract_excerpt":"Let $A(n)$ denote the $(1,n)\\text{-th}$ Fourier coefficient of a $SL(3, \\mathbb{Z})$ Hecke eigenform or the ternary divisor function $d_3(n)$. 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