On the difference between consecutive zeros of the Riemann zeta function

AbstractLet 0 < γ1 ≤ γ2 ≤ … be the imaginary part of the zeros, λ = limn(γn − γn − 1)(logγn2π) and μ = limn(γn − γn − 1)(logγn2π). Assuming the Riemann hypothesis, it is known that μ ≤ 0.68 and λ > 1. One suspects that μ = 0 and λ = +∞. The object of this note is to show that λ ≥ 1.9