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A new application of the Gram points. (English) Zbl 07109883
Summary: The Gram points \(t_n\) are defined as solutions of the equation \(\theta (t)=(n-1)\pi,\ n\in \mathbb{N}\), where \(\theta(t),\ t>0\), denotes the increment of the argument of the function \(\pi^{-s/2}\Gamma \bigl(\frac{s}{2}\bigr)\) along the segment connecting the points \(s=\frac{1}{2}\) and \(s=\frac{1}{2}+it\). In the paper, theorems on the approximation of a wide class of analytic functions by shifts \(\zeta (s+iht_k),\ h>0,\ k\in \mathbb{N}\), of the Riemann zeta-function are obtained.

MSC:
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
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