{"paper":{"title":"Summing Lambert Series in Euler's q-Exponential Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Ruiming Zhang","submitted_at":"2018-11-16T08:01:17Z","abstract_excerpt":"In the work we shall present formulas to sum Lambert series using Euler's q-exponential functions, and several Lambert series associated with well-known arithmetic functions are given as examples. These functions are: the M\\\"{o}bius $\\mu(n)$, the Euler's totient $\\varphi(n)$, Jordan's totient $J_{k}(n)$, von Mangoldt $\\Lambda(n)$, divisor function $\\sigma_{s}(n)$, the Ramanujan's sum $c_{q}(n)$ , and sum of square functions $r_{2}(n),r_{4}(n),r_{8}(n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07756","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"}