{"paper":{"title":"The Fourier expansion of \\eta(z)\\eta(2z)\\eta(3z)/\\eta(6z)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christian Kassel, Christophe Reutenauer","submitted_at":"2016-03-21T09:07:33Z","abstract_excerpt":"We compute the Fourier coefficients of the weight one modular form $\\eta(z)\\eta(2z)\\eta(3z)/\\eta(6z)$ in terms of the number of representations of an integer as a sum of two squares. We deduce a relation between this modular form and translates of the modular form $\\eta(z)^4/\\eta(2z)^2$. In the last section we use our main result to give an elementary proof of an identity by Victor Kac."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06357","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"}