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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 Matiyasevich
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.

History

Journal

Experimental mathematics

Volume

24

Pagination

150-161

Location

London, Eng.

ISSN

1058-6458

eISSN

1944-950X

Language

eng

Publication classification

C Journal article, C1 Refereed article in a scholarly journal

Copyright notice

2015, Taylor & Francis

Issue

2

Publisher

Taylor & Francis