{"paper":{"title":"Factorization Theorems for Generalized Lambert Series and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maxie D. Schmidt, Mircea Merca","submitted_at":"2017-12-02T14:25:17Z","abstract_excerpt":"We prove new variants of the Lambert series factorization theorems studied by Merca and Schmidt (2017) which correspond to a more general class of Lambert series expansions of the form $L_a(\\alpha, \\beta, q) := \\sum_{n \\geq 1} a_n q^{\\alpha n-\\beta} / (1-q^{\\alpha n-\\beta})$ for integers $\\alpha, \\beta$ defined such that $\\alpha \\geq 1$ and $0 \\leq \\beta < \\alpha$. Applications of the new results in the article are given to restricted divisor sums over several classical special arithmetic functions which define the cases of well-known, so-termed \"ordinary\" Lambert series expansions cited in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00611","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"}