{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08743","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}