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Approximation of riemanns zeta function by finite dirichlet series: A multiprecision numerical approach
journal contribution
posted on 2015-01-01, 00:00 authored by Gleb BeliakovGleb Beliakov, Y MatiyasevichThe 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.
History
Journal
Experimental mathematicsVolume
24Issue
2Pagination
150 - 161Publisher
Taylor & FrancisLocation
London, Eng.Publisher DOI
ISSN
1058-6458eISSN
1944-950XLanguage
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2015, Taylor & FrancisUsage metrics
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