Equivalents of the Riemann hypothesis involving the Gram points

The Riemann hypothesis (RH) on zeros of the zeta-function ζ(s), s=σ +it, states that all zeros of ζ(s) in the strip 0 < σ < 1 lie on the line σ =1/2. Several equivalents of RH are known. In the paper, we obtain equivalents of RH in terms of self-approximation of ζ(s) by shifts ζ(s+ihtₖ), k∈ N, where ₖ, k∈ N\ is the sequence of the Gram points.