{"paper":{"title":"Zeros of partial sums of the Dedekind zeta function of a cyclotomic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Zaharescu, Andrew Ledoan, Arindam Roy","submitted_at":"2013-07-31T23:30:56Z","abstract_excerpt":"In this article, we study the zeros of the partial sums of the Dedekind zeta function of a cyclotomic field $K$ defined by the truncated Dirichlet series \\[ \\zeta_{K, X} (s)\n  = \\sum_{\\|\\mathfrak{a}\\| \\leq X} \\frac{1}{\\|\\mathfrak{a}\\|^{s}}, \\] where the sum is to be taken over nonzero integral ideals $\\mathfrak{a}$ of $K$ and $\\|\\mathfrak{a}\\|$ denotes the absolute norm of $\\mathfrak{a}$. Specifically, we establish the zero-free regions for $\\zeta_{K, X} (s)$ and estimate the number of zeros of $\\zeta_{K, X} (s)$ up to height $T$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0065","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"}