Rigorous high-precision computation of the Hurwitz zeta function and its derivatives

@article{Johansson2014RigorousHC,
  title={Rigorous high-precision computation of the Hurwitz zeta function and its derivatives},
  author={Fredrik Johansson},
  journal={Numerical Algorithms},
  year={2014},
  volume={69},
  pages={253-270}
}
We study the use of the Euler-Maclaurin formula to numerically evaluate the Hurwitz zeta function ζ(s, a) for s,a∈ℂ$s, a \in \mathbb {C}$, 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… Expand
Error bounds for the asymptotic expansion of the Hurwitz zeta function
  • G. Nemes
  • Mathematics, Medicine
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2017
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References

SHOWING 1-10 OF 55 REFERENCES
Fast methods to compute the Riemann zeta function
An effective asymptotic formula for the Stieltjes constants
Power series expansions of Riemann’s function
...
1
2
3
4
5
...