Isolating some non-trivial zeros of Zeta

David J Platt

doi:10.1090/mcom/3198

Isolating some non-trivial zeros of Zeta

David J Platt

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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 ≤ 30,610,046,000 to an absolute precision of ±2^-102. In the process, we provide an independent veri cation of the Riemann Hypothesis to this height.

Original language	English
Pages (from-to)	2449-2467
Number of pages	19
Journal	Mathematics of Computation
Volume	86
Issue number	307
Early online date	13 Feb 2017
DOIs	https://doi.org/10.1090/mcom/3198
Publication status	Published - 6 May 2017

Keywords

Primary 11Y35
11M26

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10.1090/mcom/3198

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via American Mathematical Society at http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2017-03198-7/home.html#Additional . Please refer to any applicable terms of use of the publisher.
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AB - 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 ≤ 30,610,046,000 to an absolute precision of ±2-102. In the process, we provide an independent veri cation of the Riemann Hypothesis to this height.

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Isolating some non-trivial zeros of Zeta

Abstract

Keywords

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