Random multiplicative functions: the Selberg-Delange class

Let 1∕2≤β<1, p be a generic prime number and fβ random multiplicative function supported on the squarefree integers such that (fβ(p))p is an i.i.d. sequence of variables with distribution P(f(p)=−1)=β=1−P(f(p)=+1). Fβ Dirichlet series fβ. We prove formula involving measure-preserving transformations relates Riemann ζ Fβ, for certain values β, give application. Further, we hypothesis connected mean behavior weighted partial sum