Precalculated arrays-based algorithms for the calculation of the Riemann zeta-function

Abstract

In this paper, we continue the study of efficient algorithms for the computation of the Riemann zeta function on the complex plane. We introduce two precalculated arrays-based modifications of MB-method. We perform numerical experiments with these algorithms using Zetafast as a benchmark and apply the algorithms for the visualizations of fractal structures associated with the Riemann zeta function.

Keywords

• Riemann zeta function
• numerical algorithms
• fractal structures