{"paper":{"title":"Finite Ramanujan expansions and shifted convolution sums of arithmetical functions, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Coppola, M. Ram Murty","submitted_at":"2017-05-19T21:21:45Z","abstract_excerpt":"We continue our study of convolution sums of two arithmetical functions $f$ and $g$, of the form $\\sum_{n \\le N} f(n) g(n+h)$, in the context of heuristic asymptotic formul\\ae. Here, the integer $h\\ge 0$ is called, as usual, the {\\it shift} of the convolution sum. We deepen the study of finite Ramanujan expansions of general $f,g$ for the purpose of studying their convolution sum. Also, we introduce another kind of Ramanujan expansion for the convolution sum of $f$ and $g$, namely in terms of its shift $h$ and we compare this \\lq \\lq shifted Ramanujan expansion\\rq \\rq, with our previous finite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07193","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"}