{"paper":{"title":"The Lerch zeta function III. Polylogarithms and special values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jeffrey C. Lagarias, W.-C. Winnie Li","submitted_at":"2015-06-19T21:24:21Z","abstract_excerpt":"This paper studies algebraic and analytic structures associated with the Lerch zeta function, extending the complex variables viewpoint taken in part II. The Lerch transcendent $\\Phi(s, z, c)$ is obtained from the Lerch zeta function $\\zeta(s, a, c)$ by the change of variable $z=e^{2 \\pi i a}$. We show that it analytically continues to a maximal domain of holomorphy in three complex variables $(s, z, c)$ as a multivalued function defined over the base manifold ${\\bf C} \\times P^1({\\bf C} \\smallsetminus \\{0, 1, \\infty\\}) \\times ({\\bf C}\\smallsetminus {\\bf Z})$. and compute the monodromy functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06161","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"}