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We prove that the conjecture holds over K=Q for both the analytic rank and the p-infinity Selmer rank of E for every odd prime p. For arbitrary E/K, we show that Larsen's conjecture follows from the standard conjectures for ranks of elliptic curves, provided K has a real place or E has non-integral j-invariant."},"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":"0803.1122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-03-07T15:55:52Z","cross_cats_sorted":[],"title_canon_sha256":"63048ece37883e26e70a08bb9a0c9f5bc10c1963321579b8d0b420abd67d8f73","abstract_canon_sha256":"45b4e6e7f574cd4ac30af753a8b4e997e978dcea4171c596fa7795420a86c509"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:35.501430Z","signature_b64":"JZu2Utzks2Yx7zZDuYS7mxhpKWjEo1/dSYvopJQcLVIBn/0VaZt5uqlVYH8nWtZVOYvCNRS/C0axhS6aLAIDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56d6b080b800fb68f0e3fab6a0c9b391c66aaba0080671f94a45aac7d8ec0e19","last_reissued_at":"2026-05-18T03:12:35.500707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:35.500707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on Larsen's conjecture and ranks of elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tim Dokchitser, Vladimir Dokchitser","submitted_at":"2008-03-07T15:55:52Z","abstract_excerpt":"Let E be an elliptic curve defined over a number field K. 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