{"paper":{"title":"Distribution of the values of the derivative of the Dirichlet $L$-functions at its $a$-points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kamel Mazhouda, Mohamed Ta\\\"ib Jakhlouti","submitted_at":"2015-03-10T23:03:20Z","abstract_excerpt":"In this paper, we study the value distribution of the derivative of a Dirichlet $L$-function $L'(s,\\chi)$ at the $a$-points $\\rho_{a,\\chi}=\\beta_{a,\\chi}+i\\gamma_{a,\\chi}$ of $L(s,\\chi).$ We give an asymptotic formula for the sum $$\\sum_{\\rho_{a,\\chi};\\ 0<\\gamma_{a,\\chi}\\leq T}L'\\left(\\rho_{a,\\chi},\\chi\\right) X^{\\rho_{a,\\chi}}\\ \\ \\hbox{as}\\ \\\n  T\\longrightarrow \\infty,$$ where $X$ is a fixed positive number and $\\chi$ is a primitive character $\\mod q$. This work continues the investigations of Fujii \\cite{2,3,4}, Garunk$\\check{s}$tis \\& Steuding \\cite{7} and the authors \\cite{12}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03119","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"}