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In this paper we prove the following subconvex bound $$ L\\left(\\tfrac{1}{2}+it,\\pi\\times f\\right)\\ll_{\\pi,f,\\varepsilon} (1+|t|)^{\\frac{3}{2}-\\frac{1}{42}+\\varepsilon}. $$"},"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":"1810.00539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-01T06:01:12Z","cross_cats_sorted":[],"title_canon_sha256":"89634793c98308f42410a138779d3c070b44dac8e07c698831cc27ebb3d33588","abstract_canon_sha256":"32562604bde05046cb851caf23f9611b73d4f8c4c0e9bca99d2886f7790eca85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:25.872170Z","signature_b64":"Fp2xJVobWjxiDiXvJdfBBQzBLISdmQwahNdOWzGBDjjFf15D/RVSxjbvZm4cblEpCOcveOpHj2Iq7+ljUZPfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9df6023bb5e6054032d942326dc7a9600c2e9e2279bdebee2b355cf8508fd629","last_reissued_at":"2026-05-18T00:04:25.871426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:25.871426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subconvexity for $GL(3)\\times GL(2)$ $L$-functions in $t$-aspect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ritabrata Munshi","submitted_at":"2018-10-01T06:01:12Z","abstract_excerpt":"Let $\\pi$ be a Hecke-Maass cusp form for $SL(3,\\mathbb Z)$ and $f$ be a holomorphic (or Maass) Hecke form for $SL(2,\\mathbb{Z})$. 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