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We evaluate the degree over K of extensions of the form K(\\zeta_m, \\sqrt[n]{a}) with n\\leq m, which are obtained by adjoining a root of unity of order l^m and the l^n-th roots of a, as this is needed for computing the above density."},"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":"1107.4595","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-22T19:04:24Z","cross_cats_sorted":[],"title_canon_sha256":"2caa4457a069e46774bd9f28e491e1e511af21df2dfac27d9620ec531f086d65","abstract_canon_sha256":"17af30ebcb8c40e5fc999572f8685d5ad251c131904ee809db15fd309e8bc33e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:42.697529Z","signature_b64":"MGvqxG54PWex5w2n4Atr5WbVw5rcl30zgGyV5lzE8+J+XRCKlWwndV8dDcpyQvJesY4qMIVbdsoHYygb/226DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"deed811c5d0b5d2a47a187dda74c01e8924b63de5f806a5a6148bf746c422be5","last_reissued_at":"2026-05-18T02:51:42.697049Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:42.697049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The order of the reductions of an algebraic integer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antonella Perucca","submitted_at":"2011-07-22T19:04:24Z","abstract_excerpt":"Let K be a number field, and let a be a non-zero element of K. 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