Archiv der Mathematik

, Volume 99, Issue 1, pp 43–47 | Cite as

Erratum to: The generalized strong recurrence for non-zero rational parameters

  • Takashi Nakamura
  • Łukasz Pańkowski


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 ≠ d = a/b with |ab| ≠ 1 and gcd(a,b) = 1.

Mathematics Subject Classification

Primary 11M06 Secondary 11M26 


The Riemann zeta function Self-approximation 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and TechnologyTokyo University of Science NodaChibaJapan
  2. 2.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznanPoland

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