DOES A RANDOM WALKER MEET UNIVERSALITY?

Author:

Teerapat~SRICHAN,~Rasa~STEUDING,~J\"orn~STEUDING

2010 Mathematics Subject Classification:

11M41.

Keywords:

Brownian motion, random walk, Riemann zeta-function, universality.

Abstract:

We may interpret the absolute value of an analytic function as analytic landscape over the complex plane. Roughly speaking, Voronin's universality theorem implies that any finite analytic landscape can be found - up to an arbitrarily small error - in the analytic landscape of the Riemann zeta-function. Imagine a person somewhere lost in the analytic landscape of the zeta-function; if this guy is randomly walking around, will he find an instance where his surrounding looks like where he has started? Moreover, what variety of landscapes will his eyes catch while walking around?

Download paper:

Sric-Steu-Steu-2013

Vol. 8 (16), 2013