| Title |
Series with binomial-like coefficients for the evaluation and 3D visualization of zeta functions / |
| Authors |
Belovas, Igoris ; Sabaliauskas, Martynas |
| DOI |
10.15388/20-INFOR434 |
| Full Text |
|
| Is Part of |
Informatica.. Vilnius : Vilnius University Institute of Data Science and Digital Technologies. 2020, vol. 31, iss. 4, p. 659-680.. ISSN 0868-4952. eISSN 1822-8844 |
| Keywords [eng] |
zeta function ; asymptotic normality ; limit theorem ; efficient algorithms ; 3D visualization |
| Abstract [eng] |
In this paper, we continue the study of efficient algorithms for the computation of zeta functions on the complex plane, extending works of Coffey, \v Sle\v zevi\v cien\. e and Vep\v stas. 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. |
| Published |
Vilnius : Vilnius University Institute of Data Science and Digital Technologies |
| Type |
Journal article |
| Language |
English |
| Publication date |
2020 |
| CC license |
|
