Abstract

Voronin's Universality Theorem states grosso modo, that any non-vanishing analytic function can be uniformly approximated by certain shifts of the Riemann zeta-function zeta(s). However, the problem of obtaining a concrete approximants for a given function is computationally highly challenging. The present note deals with this problem, using a finite number n of factors taken from the Euler product definition of zeta(s). The main result of the present work is the design and implementation of a sequential and a parallel heuristic method for the computation of those approximants. The main properties of this method are: (i) the computation time grows quadratically as a function of the quotient n/m, where m is the number of coefficients calculated in one iteration of the heuristic; (ii) the error does not vary significantly as m changes and is similar to the error of the exact algorithm.