Open Access
An efficient algorithm for the Riemann zeta function
Peter Borwein
- 01 Jan 1995
39
TL;DR: A very simple class of algorithms for the computation of the Riemann-zeta function to arbitrary precision in arbitrary domains is proposed and out perform the standard methods based on Euler-Maclaurin summation.
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Abstract: A very simple class of algorithms for the computation of the Riemann-zeta function to arbitrary precision in arbitrary domains is proposed. These algorithms out perform the standard methods based on Euler-Maclaurin summation, are easier to implement and are easier to analyse.
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Modern Computer Arithmetic
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- 27 Dec 2010
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Rigorous high-precision computation of the Hurwitz zeta function and its derivatives
TL;DR: New record computations of Stieltjes constants, Keiper-Li coefficients and the first nontrivial zero of the Riemann zeta function are presented using an open source implementation of the algorithms described in this paper.
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Rigorous high-precision computation of the Hurwitz zeta function and its derivatives
TL;DR: In this paper, the Euler-Maclaurin formula was used to numerically evaluate the Hurwitz zeta function to arbitrary precision with rigorous error bounds, and the first nontrivial zero was obtained using an open source implementation of the algorithm.
Computation and theory of extended Mordell-Tornheim-Witten sums
TL;DR: This work considers some fundamental generalized Mordell{Tornheim{Witten} zeta-function values along with their derivatives, and explores connections with multiple- zeta values (MZVs), and signicantly extend methods for high-precision numerical computation of polylogarithms and their derivatives with respect to order.