High precision computation of Riemann's zeta function by the Riemann-Siegel formula, I

@article{Reyna2011HighPC,
  title={High precision computation of Riemann's zeta function by the Riemann-Siegel formula, I},
  author={Juan Arias de Reyna},
  journal={Math. Comput.},
  year={2011},
  volume={80},
  pages={995-1009}
}
We present rigorous and sharp bounds for the terms and remainder in the Riemann-Siegel formula (for a general argument, not necessarily on the critical line). This allows for the computation of ((s) and Z(t) to high precision. We also derive the Riemann-Siegel formula in a new and more direct way. 

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