{"paper":{"title":"A Ces\\`aro average for an additive problem with prime powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alessandro Languasco, Alessandro Zaccagnini","submitted_at":"2018-06-13T10:27:27Z","abstract_excerpt":"In this paper we extend and improve our results on weighted averages for the number of representations of an integer as a sum of two powers of primes. Let $1\\le \\ell_1 \\le \\ell_2$ be two integers, $\\Lambda$ be the von Mangoldt function and % \\(r_{\\ell_1,\\ell_2}(n) = \\sum_{m_1^{\\ell_1} + m_2^{\\ell_2}= n} \\Lambda(m_1) \\Lambda(m_2) \\) % be the weighted counting function for the number of representation of an integer as a sum of two prime powers. Let $N \\geq 2$ be an integer. We prove that the Ces\\`aro average of weight $k > 1$ of $r_{\\ell_1,\\ell_2}$ over the interval $[1, N]$ has a development as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04930","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"}