Path Integrals and Voronin’s Theorem on the Universality of the Riemann Zeta Function

This talk is based on work with N. Khuri and H. Ren.[1,2] The main new tools we use are theorems by Voronin on the universality properties of the Riemann Zeta function, ζ(s), in the critical strip, 1 2 < Re s < 1. Given any real continuous function, φ(x), 0 ≤ x ≤ L, we can choose a mapping, s(x), which maps the line, 0 ≤ x ≤ L, onto a line s(x) that lies in the strip 1 2 < Re s < 1, then given any ∆ > 0, we have an infinite set of integers, L, such that for all nǫL,