{"paper":{"title":"Asymptotics of Certain q-Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ruiming Zhang","submitted_at":"2018-12-08T01:01:51Z","abstract_excerpt":"In this work we study complete asymptotic expansions for the q-series $\\sum_{n=1}^{\\infty}\\frac{1}{n^{b}}q^{n^{a}}$ and $\\sum_{n=1}^{\\infty}\\frac{\\sigma_{\\alpha}(n)}{n^{b}}q^{n^{a}}$ in the scale function $(\\log q)^{n}$ as $q\\to1^{-}$, where $a>0,\\ q\\in(0,1),\\,b,\\alpha\\in\\mathbb{C}$ and $\\sigma_{\\alpha}(n)$ is the divisor function $\\sigma_{\\alpha}(n)=\\sum_{d\\vert n}d^{\\alpha}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01109","kind":"arxiv","version":1},"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"}