cp's OEIS Frontend

A356216 Decimal expansion of the real part of the first nontrivial zero of zeta'.

%I A356216 #89 Sep 23 2022 17:19:18
%S A356216 2,4,6,3,1,6,1,8,6,9,4,5,4,3,2,1,2,8,5,8,7,4,3,9,5,0,5,3,3,0,6,3,2,9,
%T A356216 1,4,4,9,2,0,7,9,3,1,3,4,5,6,7,3,2,3,4,7,5,0,2,2,2,1,7,3,7,0,7,2,7,1,
%U A356216 1,7,5,0,8,6,7,1,0,2,6,3,7,1,1,9,4,8,2,4,6,8,6,1,3,2,8,3,5,5,4,2,6,7,0,5,4,1,5,5,1,0,4,1,7,8,8,8,6,1,9,2,3,5,0,7,4,0,4
%N A356216 Decimal expansion of the real part of the first nontrivial zero of zeta'.
%C A356216 The nontrivial zero of zeta' with the smallest imaginary part is 2.4631618694543212... + i*23.2983204927628579...
%C A356216 The Riemann Hypothesis is equivalent to the assertion that zeta' (the derivative of the Riemann zeta function) has no nontrivial zero in the half-plane Re(z) < 1/2 (there are trivial zeros, e.g., -2.717262829204574...).
%H A356216 Norman Levinson and Hugh L. Montgomery, <a href="https://doi.org/10.1007/BF02392141">Zeros of the derivatives of the Riemann zeta-function</a>, Acta Mathematica, Vol. 133 (1974), pp. 49-65; <a href="http://archive.ymsc.tsinghua.edu.cn/pacm_download/117/6174-11511_2006_Article_BF02392141.pdf">alternative link</a>.
%e A356216 2.463161869454321285874395053306329144920793134567323475022217370727117508671...
%t A356216 RealDigits[Re[x /. FindRoot[Derivative[1][Zeta][x], {x, 2 + 23*I}, WorkingPrecision -> 100]]][[1]] (* _Amiram Eldar_, Aug 14 2022 *)
%Y A356216 Cf. A356092.
%K A356216 nonn,cons
%O A356216 1,1
%A A356216 _Benoit Cloitre_, Aug 13 2022