LAUSR

The Gram points $$t_n$$tn are defined as solutions of the equation $$\theta (t)=(n-1)\pi $$θ(t)=(n-1)π, $$n\in \mathbb {N}$$n∈N, where $$\theta (t)$$θ(t), $$t>0$$t>0, denotes the increment of the argument of the function $$\pi ^{-s/2}\Gamma \left( \frac{s}{2}\right) $$π-s/2Γs2 along the segment connecting the points $$s=\frac{1}{2}$$s=12 and $$s=\frac{1}{2}+it$$s=12+it. In the paper, theorems on the approximation of a wide class of analytic functions by shifts $$\zeta (s+iht_k)$$ζ(s+ihtk), $$h>0$$h>0, $$k\in \mathbb {N}$$k∈N, of the Riemann zeta-function are obtained.