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We develop various asymptotic relations between the Riemann zeta function ζ(s) and the interpolation errors of Lagrange and Hermite interpolation to functions like ${\left|y\right|}^s$ and $y^{2m}log\left|y\right|$. We show that the interpolation nodes of these interpolation processes include zeros of Gegenbauer and Hermite polynomials and polynomials with equidistant zeros. Similar results are valid for the Dirichlet beta function β(s) as well. So the results of the monograph serve as the bridge between the theory of zeta functions and...