{"paper":{"title":"Mahler's Measure and the Dilogarithm (II)","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.NT","authors_text":"David W. Boyd, Fernando Rodriguez-Villegas, Nathan M. Dunfield","submitted_at":"2003-08-05T19:31:13Z","abstract_excerpt":"We continue to investigate the relation between the Mahler measure of certain two variable polynomials, the values of the Bloch--Wigner dilogarithm $D(z)$ and the values $\\zeta_F(2)$ of zeta functions of number fields. Specifically, we define a class $\\A$ of polynomials $A$ with the property that $\\pi m(A)$ is a linear combination of values $D$ at algebraic arguments. For many polynomials in this class the corresponding argument of $D$ is in the Bloch group, which leads to formulas expressing $\\pi m(A)$ as a linear combination with unspecified rational coefficients of $V_F$ for certain number "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0308041","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0308041/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}