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Zeroes of Riemann's zeta function on the critical line with 20000 decimal digits accuracy

Deakin University
Gleb Beliakov (Associated with, Aggregated by) Prof Gleb Beliakov (Associated with, Aggregated by)
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ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rfr_id=info%3Asid%2FANDS&rft_id=hdl.handle.net/10536/DRO/DU:30051725&rft.title=Zeroes of Riemann's zeta function on the critical line with 20000 decimal digits accuracy&rft.identifier=hdl.handle.net/10536/DRO/DU:30051725&rft.publisher=Deakin University&rft.description=The first 12000 zeroes of Riemann's zeta function on the critical line with 20000 decimal digits accuracy. Format: the zeroes are in text file listed consecutively in decimal representation, each zero starts on a new line.Zeroes of zeta function presented in this file were calculated on MASSIVE cluster (www.massive.org.au) using Python and packages MPmath version 0.17 and gmpy version 2.1, with a Newton based algorithm proposed by Fredrik Johansson with precision set to 20000 decimal digits. Partial recalculation with higher precision didn't show any loss of accuracy so we expect that the values are correct up to, possibly, a few last digits. We express our thanks to Fredrik Johansson for this algorithm and for development of MPmath as well.&rft.creator=Gleb Beliakov&rft.creator=Prof Gleb Beliakov&rft.date=2018&rft.relation=http://logic.pdmi.ras.ru/~yumat/personaljournal/artlessmethod/talks/leicester2012/leicester_2012_full.pdf&rft.relation=http://logic.pdmi.ras.ru/~yumat/personaljournal/artlessmethod/texts/short_introduction.pdf&rft_rights=Copyright owner&rft_subject=Riemann's zeta function&rft_subject=Riemann's zeroes&rft_subject=8th Hilbert problem&rft_subject=Real and Complex Functions (incl. Several Variables)&rft_subject=MATHEMATICAL SCIENCES&rft_subject=PURE MATHEMATICS&rft_subject=Expanding Knowledge in the Mathematical Sciences&rft_subject=EXPANDING KNOWLEDGE&rft_subject=EXPANDING KNOWLEDGE&rft.type=dataset&rft.language=English Access the data
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gleb.beliakov@deakin.edu.au

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The first 12000 zeroes of Riemann's zeta function on the critical line with 20000 decimal digits accuracy. Format: the zeroes are in text file listed consecutively in decimal representation, each zero starts on a new line.

Zeroes of zeta function presented in this file were calculated on MASSIVE cluster (www.massive.org.au) using Python and packages MPmath version 0.17 and gmpy version 2.1, with a Newton based algorithm proposed by Fredrik Johansson with precision set to 20000 decimal digits. Partial recalculation with higher precision didn't show any loss of accuracy so we expect that the values are correct up to, possibly, a few last digits. We express our thanks to Fredrik Johansson for this algorithm and for development of MPmath as well.

Notes

This dataset was automatically generated using Python and packages MPmath version 0.17 and gmpy version 2.1.

Data time period: 2011

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8th Hilbert problem | Expanding Knowledge | Expanding Knowledge | Expanding Knowledge in the Mathematical Sciences | Mathematical Sciences | Pure Mathematics | Real and Complex Functions (Incl. Several Variables) | Riemann's zeroes | Riemann's zeta function |

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