{"paper":{"title":"On multivariable averages of divisor functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"L\\'aszl\\'o T\\'oth, Wenguang Zhai","submitted_at":"2017-11-12T09:17:31Z","abstract_excerpt":"We deduce asymptotic formulas for the sums $\\sum_{n_1,\\ldots,n_r\\le x} f(n_1\\cdots n_r)$ and $\\sum_{n_1,\\ldots,n_r\\le x} f([n_1\\cdots n_r])$, where $r\\ge 2$ is a fixed integer, $[n_1,\\ldots,n_r]$ stands for the least common multiple of the integers $n_1,\\ldots,n_r$ and $f$ is one of the divisor functions $\\tau_{1,k}(n)$ ($k\\ge 1$), $\\tau^{(e)}(n)$ and $\\tau^*(n)$. Our formulas refine and generalize a result of Lelechenko (2014). A new generalization of the Busche-Ramanujan identity is also pointed out."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04257","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"}