ACTA issues

## Functional limits of zeta type processes

Werner Ehm

Acta Sci. Math. (Szeged) 74:1-2(2008), 381-398
6021/2009

 Abstract. The Riemann zeta process is a stochastic process $\{Z(\sigma ), \sigma >1\}$ with independent increments and marginal distributions whose characteristic functions are proportional to the Riemann zeta function along vertical lines ${\msbm R}e s = \sigma$. We establish functional limit theorems for the zeta process and other related processes as arguments $\sigma$ approach the pole at $s=1$ of the zeta function (from above). AMS Subject Classification (1991): 60G51, 60F17, 11N37 Keyword(s): Erdős--Kac theorem, functional limit theorem, geometric process, Riemann zeta function, zeta process Received August 14, 2007, and in revised form March 13, 2008. (Registered under 6021/2009.)