Open AccessAt Least One-Third of Zeros of Riemann's Zeta-Function are on σ = ½
Author(s) -
Norman Levinson
Publication year - 1974
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.71.4.1013
Subject(s) - riemann zeta function , riemann hypothesis , functional equation , mathematics , arithmetic zeta function , sigma , function (biology) , particular values of riemann zeta function , riemann xi function , mathematical analysis , prime zeta function , pure mathematics , mathematical physics , physics , differential equation , quantum mechanics , biology , evolutionary biology
Starting from the derivative of the functional equation of the zeta-function, it is shown that at least one-third of the zeros of the zeta-function are on the line σ = ½.