Corrigendum for "The generalized strong recurrence for non-zero rational parameters" Archiv der Mathematik 95 (2010), 549-555

Abstract

In the present paper, we prove that self-approximation of $\log \zeta (s)$ with $d=0$ is equivalent to the Riemann Hypothesis. Next, we show self-approximation of $\log \zeta (s)$ with respect to all nonzero real numbers $d$. Moreover, we partially filled a gap existing in "The strong recurrence for non-zero rational parameters" and prove self-approximation of $\zeta(s)$ for $0 \ne d=a/b$ with $|a-b|\ne 1$ and $\gcd(a,b)=1$.