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 ≠ d = a/b with |a−b| ≠ 1 and gcd(a,b) = 1.
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T. Nakamura was partially supported by JSPS Grants 21740024. Ł. Pańkowski was partially supported by the grant no. N N201 6059 40 from National Science Centre.
The online version of the original article can be found under doi:10.1007/s00013-010-0205-2.
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Nakamura, T., Pańkowski, Ł. Erratum to: The generalized strong recurrence for non-zero rational parameters. Arch. Math. 99, 43–47 (2012). https://doi.org/10.1007/s00013-012-0392-0
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DOI: https://doi.org/10.1007/s00013-012-0392-0