A new application of the gram points.

The Gram points t n are defined as solutions of the equation θ (t) = (n - 1) π , n ∈ N , where θ (t) , t > 0 , denotes the increment of the argument of the function π - s / 2 Γ s 2 along the segment connecting the points s = 1 2 and s = 1 2 + i t . In the paper, theorems on the approximation of a wide class of analytic functions by shifts ζ (s + i h t k) , h > 0 , k ∈ N , of the Riemann zeta-function are obtained. [ABSTRACT FROM AUTHOR]