{"paper":{"title":"Lacunarity of Han-Nekrasov-Okounkov $q$-series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Katherine Gallagher, Katja Vassilev, Lucia Li","submitted_at":"2018-07-12T12:39:41Z","abstract_excerpt":"A power series is called lacunary if `almost all' of its coefficients are zero. Integer partitions have motivated the classification of lacunary specializations of Han's extension of the Nekrasov-Okounkov formula. More precisely, we consider the modular forms \\[F_{a,b,c}(z) := \\frac{\\eta(24az)^a \\eta(24acz)^{b-a}}{\\eta(24z)},\\] defined in terms of the Dedekind $\\eta$-function, for integers $a,c \\geq 1$ where $b \\geq 1$ is odd throughout. Serre determined the lacunarity of the series when $a = c = 1$. Later, Clader, Kemper, and Wage extended this result by allowing $a$ to be general, and comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04576","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"}