{"paper":{"title":"Tests of conjectures on multiple Watson values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"David Broadhurst","submitted_at":"2015-04-29T20:15:32Z","abstract_excerpt":"I define multiple Watson values (MWVs) as iterated integrals, on the interval $x\\in[0,1]$, of the 6 differential forms $A=d\\log(x)$, $B=-d\\log(1-x)$, $T=-d\\log(1-z_1x)$, $U=-d\\log(1-z_2x)$, $V=-d\\log(1-z_3x)$ and $W=-d\\log(1-z_4x)$, where $z_1=\\gamma^2$, $z_2=\\gamma/(1+\\gamma)$, $z_3=\\gamma^2/(1-\\gamma)$ and $z_4=\\gamma=2\\sin(\\pi/14)$ solves the cubic $(1-\\gamma^2)(1-\\gamma)=\\gamma$. Following a suggestion by Pierre Deligne, I conjecture that the dimension of the space of ${\\mathbb Z}$-linearly independent MWVs of weight $w$ is the number $D_w$ generated by $1/(1-2x-x^2-x^3)=1+\\sum_{w>0}D_w x^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08007","kind":"arxiv","version":1},"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"}