Pub. online:9 Nov 2020Type:Research ArticleOpen Access
Volume 31, Issue 4 (2020), pp. 659–680
In this paper, we continue the study of efficient algorithms for the computation of zeta functions on the complex plane, extending works of Coffey, Šleževičienė and Vepštas. We prove a central limit theorem for the coefficients of the series with binomial-like coefficients used for evaluation of the Riemann zeta function and establish the rate of convergence to the limiting distribution. An asymptotic expression is derived for the coefficients of the series. We discuss the computational complexity and numerical aspects of the implementation of the algorithm. In the last part of the paper we present our results on 3D visualizations of zeta functions, based on series with binomial-like coefficients. 3D visualizations illustrate underlying structures of surfaces and 3D curves associated with zeta functions.