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Lagrange Interpolation and New Asymptotic Formulae for the Riemann Zeta Function

Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 13)

Abstract

An asymptotic representation for the Riemann zeta function ζ(s) in terms of the Lagrange interpolation error of some function f s,2N at the Chebyshev nodes is found. The representation is based on new error formulae for the Lagrange polynomial interpolation to a function of the form \(f(y) ={ \int \nolimits \nolimits }_{\mathbb{R}} \frac{\varphi (t)} {t-iy}\mathrm{d}t.\) As the major application of this result, new criteria for ζ(s)=0 and ζ(s)≠0 in the critical strip 0<Re s<1 are given.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Hampton UniversityVAUSA

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