{"paper":{"title":"Zeros of Dirichlet series with periodic coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andreas Weingartner, Eric Saias","submitted_at":"2008-07-04T15:48:39Z","abstract_excerpt":"Let $a=(a_n)_{n\\ge 1}$ be a periodic sequence, $F_a(s)$ the meromorphic continuation of $\\sum_{n\\ge 1} a_n/n^s$, and $N_a(\\sigma_1, \\sigma_2, T)$ the number of zeros of $F_a(s)$, counted with their multiplicities, in the rectangle $\\sigma_1 < \\Re s < \\sigma_2$, $|\\Im s | \\le T$. We extend previous results of Laurin\\v{c}ikas, Kaczorowski, Kulas, and Steuding, by showing that if $F_a(s)$ is not of the form $P(s) L_{\\chi} (s)$, where $P(s)$ is a Dirichlet polynomial and $L_{\\chi}(s)$ a Dirichlet L-function, then there exists an $\\eta=\\eta(a)>0$ such that for all $1/2 < \\sigma_1 < \\sigma_2 < 1+\\et"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0783","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"}