DOES A RANDOM WALKER MEET UNIVERSALITY?
Author:


2010 Mathematics Subject Classification:

11M41.

Keywords:

Brownian motion, random walk, Riemann zetafunction, 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 zetafunction. Imagine a person somewhere lost in the analytic landscape of the zetafunction; 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?

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Vol. 8 (16), 2013
