{"paper":{"title":"A study of elliptic gamma function and allies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.KT","math.MP"],"primary_cat":"math.NT","authors_text":"Vicen\\c{t}iu Pa\\c{s}ol, Wadim Zudilin","submitted_at":"2017-12-30T23:59:35Z","abstract_excerpt":"We study analytic and arithmetic properties of the elliptic gamma function $$ \\prod_{m,n=0}^\\infty\\frac{1-x^{-1}q^{m+1}p^{n+1}}{1-xq^mp^n}, \\qquad |q|,|p|<1, $$ in the regime $p=q$; in particular, its connection with the elliptic dilogarithm and a formula of S. Bloch. We further extend the results to more general products by linking them to non-holomorphic Eistenstein series and, via some formulae of D. Zagier, to elliptic polylogarithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00210","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"}