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

Matiyasevich, Yuri and Beliakov, Gleb 2011, Zeroes of Riemann's zeta function on the critical line with 20000 decimal digits accuracy [data collection], Study of Riemann's zeta function, the 8th Hilbert problem.

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beliakov_dataset_2013.zip beliakov_dataset_2013.zip Click to show the corresponding preview/stream application/x-zip 121.65MB 52

Field of Research 010111 Real and Complex Functions (incl Several Variables)
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
Name of data collection Zeroes of Riemann's zeta function on the critical line with 20000 decimal digits accuracy
Creator(s) Matiyasevich, Yuri
Beliakov, GlebORCID iD for Beliakov, Gleb orcid.org/0000-0002-9841-5292
Contributor(s) Beliakov, GlebORCID iD for Beliakov, Gleb orcid.org/0000-0002-9841-5292
Related institution(s) ArmNGI (Armenian National Grid Initiative Foundation)
Isaac Newton Institute for Mathematical Sciences, UK
LACL (Laboratoire d'Algorithmique, Complexite et Logique de Universite Paris-Est Creteil)
LIAFA (Laboratorie d'Informatique Algorithmique: Fondements et Applications, supported jointly by the French National Centre for Scientific Research (CNRS) and the University Paris Diderot - Paris 7)
SPIIRAS (St. Petersburg Institute for Informatics and Automation of RAS)
Wolfram Research
Date completed 2011
Material type text
ANDS collection type dataset
Collection start date 2011
Project name Study of Riemann's zeta function, the 8th Hilbert problem
Project Description The project aims at computing Riemann's zeroes with high accuracy through an analysis of large determinants using Matyasievich's Artless method.  Location of Riemann's zeroes is the famous 8th Hilbert problem, and one of Clay's institute millennium problems.
Description of resource 120Mb, 12000 items
Keyword(s) Riemann's zeta function
Riemann's zeroes
8th Hilbert problem
Language eng
Summary 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.
General notes This dataset was automatically generated using Python and packages MPmath version 0.17 and gmpy version 2.1.
Contact details (email) gleb.beliakov@deakin.edu.au
Access conditions There are no access restrictions currently applied to the research data.
Copyright clearance Copyright owner
Persistent URL http://hdl.handle.net/10536/DRO/DU:30051725

 
Unless expressly stated otherwise, the copyright for items in DRO is owned by the author, with all rights reserved.

Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.

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Created: Wed, 03 Apr 2013, 10:33:36 EST by Allison Moloney

Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.