%0 Generic %1 johansson2013rigorous %A Johansson, Fredrik %D 2013 %K computation high hurwitz precision rigor %T Rigorous high-precision computation of the Hurwitz zeta function and its derivatives %U http://arxiv.org/abs/1309.2877 %X We study the use of the Euler-Maclaurin formula to numerically evaluate the Hurwitz zeta function $\zeta(s,a)$ for $s, a C$, along with an arbitrary number of derivatives with respect to $s$, to arbitrary precision with rigorous error bounds. Techniques that lead to a fast implementation are discussed. We present new record computations of Stieltjes constants, Keiper-Li coefficients and the first nontrivial zero of the Riemann zeta function, obtained using an open source implementation of the algorithms described in this paper.

@misc{johansson2013rigorous, abstract = {We study the use of the Euler-Maclaurin formula to numerically evaluate the Hurwitz zeta function $\zeta(s,a)$ for $s, a \in \mathbb{C}$, along with an arbitrary number of derivatives with respect to $s$, to arbitrary precision with rigorous error bounds. Techniques that lead to a fast implementation are discussed. We present new record computations of Stieltjes constants, Keiper-Li coefficients and the first nontrivial zero of the Riemann zeta function, obtained using an open source implementation of the algorithms described in this paper.}, added-at = {2013-12-23T07:07:02.000+0100}, author = {Johansson, Fredrik}, biburl = {https://www.bibsonomy.org/bibtex/2a3101d8f1e10d33dddb04d1c888c6586/aeu_research}, description = {Rigorous high-precision computation of the Hurwitz zeta function and its derivatives}, interhash = {774277d16f916a327ee35b64913da744}, intrahash = {a3101d8f1e10d33dddb04d1c888c6586}, keywords = {computation high hurwitz precision rigor}, note = {cite arxiv:1309.2877Comment: 15 pages, 2 figures}, timestamp = {2013-12-24T01:12:40.000+0100}, title = {Rigorous high-precision computation of the Hurwitz zeta function and its derivatives}, url = {http://arxiv.org/abs/1309.2877}, year = 2013 }