First Zeros of the Riemann Zeta Function, and Zeros Computation at Very Large Height
نویسنده
چکیده
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 different height, while collecting statistics in these zones. For example, we were able to compute two billion zeros from the 10-th zero of the Riemann Zeta function.
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