Approximation of riemanns zeta function by finite dirichlet series: A multiprecision numerical approach

Beliakov, Gleb and Matiyasevich, Yuri 2015, Approximation of riemanns zeta function by finite dirichlet series: A multiprecision numerical approach, Experimental mathematics, vol. 24, no. 2, pp. 150-161, doi: 10.1080/10586458.2014.976801.

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Title Approximation of riemanns zeta function by finite dirichlet series: A multiprecision numerical approach
Author(s) Beliakov, GlebORCID iD for Beliakov, Gleb orcid.org/0000-0002-9841-5292
Matiyasevich, Yuri
Journal name Experimental mathematics
Volume number 24
Issue number 2
Start page 150
End page 161
Total pages 12
Publisher Taylor & Francis
Place of publication London, Eng.
Publication date 2015
ISSN 1058-6458
1944-950X
Keyword(s) Science & Technology
Physical Sciences
Mathematics
L-function
Riemann hypothesis
zeta function
PARTIAL-SUMS
ZEROS
SECTIONS
Summary The finite Dirichlet series of the title are defined by the condition that they vanish at as many initial zeros of the zeta function as possible. It turns out that such series can produce extremely good approximations to the values of Riemanns zeta function inside the critical strip. In addition, the coefficients of these series have remarkable number-theoretical properties discovered in large-scale high-precision numerical experiments. So far, we have found no theoretical explanation for the observed phenomena.
Language eng
DOI 10.1080/10586458.2014.976801
Field of Research 010301 Numerical Analysis
080205 Numerical Computation
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2015, Taylor & Francis
Persistent URL http://hdl.handle.net/10536/DRO/DU:30074245

Document type: Journal Article
Collection: School of Information Technology
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