Bohr–Jessen process and functional limit theorem

Abstract

The Bohr–Jessen limit theorem states that for each σ>12, there exists an asymptotic probability distribution of logζ(σ+-1⋅). Here ζ(⋅) is the Riemann zeta function, and logζ(⋅) is a primitive function of ζ'/ζ on some simply connected domain of C. In this paper, we generalize this limit theorem to a functional limit theorem and show a similar limit theorem for a continuous process {logζ(σ+-1⋅)}σ>1/2, which we call the Bohr–Jessen functional limit theorem.