Universality of compositions involving Gram points

Abstract. Gram points \(t_k\) are solutions of the equation \(\theta(t)=(k-1)\pi\), where \(\theta(t)\) is the increment of the argument of the function \(\pi^{-s/2}\Gamma(s/2)\) along the segment connecting the points \(1/2\) and \(1/2+it\). In the paper, we consider approximation of analytic functions defined in the strip \(D=\{s\in \mathbb{C}: 1/2 < \sigma <1\}\) by shifts \(F(\zeta(s+ih t_k))\), \(h>0\), and \(\zeta(s)\) is the Riemann zeta-function, for some classes of operators \(F\) in the space of analytic on \(D\) functions. It is obtained that the sets of such shifts approximating a given analytic function is infinite. For proofs, a probabilistic approach is applied.