{"paper":{"title":"Bombieri-type theorem for convolution of arithmetic functions on Number field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anirban Mukhopadhyay, Pranendu Darbar","submitted_at":"2018-04-11T22:24:43Z","abstract_excerpt":"Let $K$ be an imaginary quadratic number field of class number one and $\\mathcal{O}_K$ be its ring of integers. We show that, if the arithmetic functions $f, g:\\mathcal{O}_K\\rightarrow \\mathbb{C}$ both have level of distribution $\\vartheta$ for some $0<\\vartheta\\leq 1/2$ then the Dirichlet convolution $f*g$ also have level of distribution $\\vartheta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04246","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"}