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We prove a subconvexity bound $$ L\\left(\\frac{1}{2},\\pi\\otimes \\chi\\right)\\ll_{p,\\pi,\\varepsilon} \\mathfrak{q}^{3/4-3/40+\\varepsilon} $$ for any $\\varepsilon>0$, where the dependence of the implied constant on $p$ is explicit and polynomial. We obtain this result by applying the circle method of Kloosterman's version, summation formulas of Poisson and Voronoi's type and a conductor lowering mechanism introduc"},"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":"1803.10973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-29T09:15:58Z","cross_cats_sorted":[],"title_canon_sha256":"ad191da90432f7eb159da4b60101758a4e108d4feed0ad9b8d38b95fd6abf2f8","abstract_canon_sha256":"dbe12c77ae3985e4685c8ea9f3ac724a2080514da5570c1b8f2241fb36fdebc9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:49.635498Z","signature_b64":"TY/veszTExH7icSGn814ixfWX6qwcVVHO3c6oDwiN15QpRic3Kjzz7gxHxoUo1Clkk+aaC/b98IbtoaOVhnxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"020dcb2d2cb3f820310519e726dc16b2237e399c7814af5028303dc72925f9f1","last_reissued_at":"2026-05-18T00:19:49.634771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:49.634771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds for $GL_3$ $L$-functions in depth aspect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qingfeng Sun, Rui Zhao","submitted_at":"2018-03-29T09:15:58Z","abstract_excerpt":"Let $f$ be a Hecke-Maass cusp form for $SL_3(\\mathbb{Z})$ and $\\chi$ a primitive Dirichlet character of prime power conductor $\\mathfrak{q}=p^{\\kappa}$ with $p$ prime and $\\kappa\\geq 10$. We prove a subconvexity bound $$ L\\left(\\frac{1}{2},\\pi\\otimes \\chi\\right)\\ll_{p,\\pi,\\varepsilon} \\mathfrak{q}^{3/4-3/40+\\varepsilon} $$ for any $\\varepsilon>0$, where the dependence of the implied constant on $p$ is explicit and polynomial. 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