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In order to do this we investigate the measure of a more general Laurent polynomial $P_{a,b,c}(x,y)=a(x+1/x)+b(y+1/y)+c$ and show that the wanted quantity $m(P)$ is related to a \"half-Mahler\" measure of $\\tilde P(x,y)=P_{\\sqrt{7},1,3}(x,y)$. In the finale we use the modular parametrization of the elliptic curve $\\tilde P(x,y)=0$, again of conductor 21, due to Ramanujan and the Mellit--Brunault formula for the regulator"},"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":"1507.08743","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-31T03:35:34Z","cross_cats_sorted":["math.AG","math.CA","math.KT"],"title_canon_sha256":"b9dbc16174c2721516b0a34ed5030f50b949c4b862966da3a8f845eb51898aeb","abstract_canon_sha256":"ae1737e859d6ea35079b120f18016065538e886abafd803c8f3c88d36122b64c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:52.609537Z","signature_b64":"UMHGAbBhT1nPE2GaNIKG5kbChdiQNCdXADyGDG1OEk+tTXapwqcwzUhENuy613+pLjFif/ie2TnNp+BvhKZFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd06b995341f91df217c323dfb4566dcf0335bdf56d15f3247e4c85f2c6f4abc","last_reissued_at":"2026-05-18T01:17:52.608852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:52.608852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Further explorations of Boyd's conjectures and a conductor 21 elliptic curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CA","math.KT"],"primary_cat":"math.NT","authors_text":"Detchat Samart, Matilde Lal\\'in, Wadim Zudilin","submitted_at":"2015-07-31T03:35:34Z","abstract_excerpt":"We prove that the (logarithmic) Mahler measure $m(P)$ of $P(x,y)=x+1/x+y+1/y+3$ is equal to the $L$-value $2L'(E,0)$ attached to the elliptic curve $E:P(x,y)=0$ of conductor 21. 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