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EXPLICIT ZERO‐FREE REGIONS FOR DIRICHLET L ‐FUNCTIONS
Author(s) -
Kadiri Habiba
Publication year - 2018
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579318000037
Subject(s) - mathematics , zero (linguistics) , modulo , dirichlet distribution , character (mathematics) , pure mathematics , value (mathematics) , function (biology) , dirichlet's energy , dirichlet l function , dirichlet series , combinatorics , mathematical analysis , geometry , boundary value problem , statistics , philosophy , linguistics , evolutionary biology , biology
Let L ( s , χ ) be the Dirichlet L ‐function associated to a non‐principal primitive character χ modulo q with 3 ⩽ q ⩽ 400 000 . We prove a new explicit zero‐free region for L ( s , χ ) : L ( s , χ ) does not vanish in the region Re s ⩾ 1 − 1 / ( R log ( q max ( 1 , | Im s | ) ) ) with R = 5 . 60 . This improves a result of McCurley where 9 . 65 was shown to be an admissible value for R .