The 10 13 first zeros of the Riemann Zeta function , and zeros computation at very large height

@inproceedings{Xavier2004The11,
  title={The 10 13 first zeros of the Riemann Zeta function , and zeros computation at very large height},
  author={Xavier},
  year={2004}
}
In this paper, we present an optimization of Odlyzko and Schönhage algorithm that computes efficiently Zeta function at large height on the critical line, together with computation of zeros of the Riemann Zeta function thanks to an implementation of this technique. The first family of computations consists in the verification of the Riemann Hypothesis on all the first 10 non trivial zeros. The second family of computations consists in verifying the Riemann Hypothesis at very large height for… CONTINUE READING
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Referenced Papers

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Showing 1-10 of 28 references

Fast algorithms for multiple evaluations of the Riemann zeta-function

  • A. M. Odlyzko, A. Schönhage
  • Trans. Amer. Math. Soc., (309)
  • 1988
Highly Influential
20 Excerpts

The 1020-th zero of the Riemann zeta function and 175 million of its neighbors

  • A. M. Odlyzko
  • Available at URL= http://www.dtc.umn.edu…
  • 1992
Highly Influential
10 Excerpts

Sharper bounds for the Chebyshev functions θ(x) and ψ(x)

  • J. B. Rosser, L. Schoenfeld
  • Math. Comput., 29:243–269
  • 1975
Highly Influential
3 Excerpts

Zetagrid - computational verification of the Riemann hypothesis

  • S. Wedeniwski
  • In Conference in Number Theory in Honour of…
  • 2003

The 1022-th zero of the Riemann zeta function

  • A. M. Odlyzko
  • M. van Frankenhuysen and M. L. Lapidus, editors…
  • 2001
3 Excerpts

Autour de la fonction qui compte les nombres premiers

  • P. Dusart
  • PhD thesis, Universit de Limoges
  • 1998
1 Excerpt

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