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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
DOI: https://doi.org/10.1090/mcom/3198
Published electronically: February 13, 2017
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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
Email: dave.platt@bris.ac.uk

DOI: https://doi.org/10.1090/mcom/3198
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

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