On an equality equivalent to the Riemann hypothesis - Volchkov, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
We prove that the Riemann hypothesis on zeros of the zeta function ζ(s) is equivalent to the equality _0^∞ 1 - 12t^2 (1 + 4t^2 )^3 dt _1/2^∞ |(σ + it)|dσ = π 3 - γ 32 , where γ = _N → ∞ ( _n = 1^N 1n - N ) is the Euler constant.