{"paper":{"title":"Value-distribution of cubic Hecke $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alia Hamieh, Amir Akbary","submitted_at":"2018-05-02T10:53:01Z","abstract_excerpt":"Let $k=\\mathbb{Q}(\\sqrt{-3})$, and let $c\\in \\mathfrak{O}_k$ be a square free algebraic integer such that $c\\equiv 1~({\\rm mod}~{\\langle9\\rangle})$. Let $\\zeta_{k(c^{1/3})}(s)$ be the Dedekind zeta function of the cubic field $k(c^{1/3})$ and $\\zeta_k(s)$ be the Dedekind zeta function of $k$. For fixed real $\\sigma>1/2$, we obtain asymptotic distribution functions $F_{\\sigma}$ for the values of the logarithm and the logarithmic derivative of the Artin $L$-functions \\begin{equation*} L_c(\\sigma)= \\frac{\\zeta_{k(c^{1/3})}(\\sigma)}{\\zeta_k(\\sigma)}, \\end{equation*} as $c$ varies. Moreover, we exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00724","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"}