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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Ganzburg, M.I. (2012). Lagrange Interpolation and New Asymptotic Formulae for the Riemann Zeta Function. In: Neamtu, M., Schumaker, L. (eds) Approximation Theory XIII: San Antonio 2010. Springer Proceedings in Mathematics, vol 13. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0772-0_6
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DOI: https://doi.org/10.1007/978-1-4614-0772-0_6
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