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Mathematics of Computation

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Isolating some non-trivial zeros of zeta

Author: David J. Platt
Journal: Math. Comp. 86 (2017), 2449-2467
MSC (2010): Primary 11Y35, 11M26
Published electronically: February 13, 2017
MathSciNet review: 3647966
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Abstract: We describe a rigorous algorithm to compute Riemann’s zeta function on the half line and its use to isolate the non-trivial zeros of zeta with imaginary part $\leq 30,610,046,000$ to an absolute precision of $\pm 2^{-102}$. In the process, we provide an independent verification of the Riemann Hypothesis to this height.

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Additional Information

David J. Platt
Affiliation: Heilbronn Institute for Mathematical Research, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
MR Author ID: 1045993

Received by editor(s): March 17, 2015
Received by editor(s) in revised form: March 29, 2016
Published electronically: February 13, 2017
Article copyright: © Copyright 2017 American Mathematical Society