1.Department of Mathematics, Faculty of Science and Technology,Tokyo University of Science Noda,Chiba,Japan;2.Faculty of Mathematics and Computer Science,Adam Mickiewicz University,Poznan,Poland
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.
