{"paper":{"title":"Eichler integrals of Eisenstein series as $q$-brackets of weighted $t$-hook functions on partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ian Wagner, Kathrin Bringmann, Ken Ono","submitted_at":"2020-09-15T17:21:53Z","abstract_excerpt":"We consider the $t$-hook functions on partitions $f_{a,t}: \\mathcal{P}\\rightarrow \\mathbb{C}$ defined by $$ f_{a,t}(\\lambda):=t^{a-1} \\sum_{h\\in \\mathcal{H}_t(\\lambda)}\\frac{1}{h^a}, $$ where $\\mathcal{H}_t(\\lambda)$ is the multiset of partition hook numbers that are multiples of $t$. The Bloch-Okounkov $q$-brackets $\\langle f_{a,t}\\rangle_q$ include Eichler integrals of the classical Eisenstein series. For even $a\\geq 2$, we show that these $q$-brackets are natural pieces of weight $2-a$ sesquiharmonic and harmonic Maass forms, while for odd $a\\leq -1,$ we show that they are holomorphic quant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07236","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/2009.07236/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"}