Archiv der Mathematik

, Volume 95, Issue 6, pp 549–555 | Cite as

The generalized strong recurrence for non-zero rational parameters



The strong recurrence is equivalent to the Riemann hypothesis. On the other hand, the generalized strong recurrence holds for any irrational number. In this paper, we show the generalized strong recurrence for all non-zero rational numbers.

Mathematics Subject Classification (2000)

Primary 11M06 Secondary 11M26 


Generalized strong recurrence Riemann hypothesis Riemann zeta function 


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© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and TechnologyTokyo University of ScienceNoda, ChibaJapan

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