cp's OEIS Frontend

A356092 Decimal expansion of the imaginary part of the first nontrivial zero of zeta'.

%I A356092 #40 Aug 15 2022 05:13:53
%S A356092 2,3,2,9,8,3,2,0,4,9,2,7,6,2,8,5,7,9,0,2,0,1,0,9,6,1,6,2,6,5,9,7,8,4,
%T A356092 7,0,5,0,5,9,5,7,6,3,9,0,0,2,8,8,3,4,9,0,2,1,4,3,0,6,9,0,4,1,0,2,8,8,
%U A356092 6,9,2,0,7,8,2,5,0,8,9,3,9,2,6,2,4,4,5,2,4,1,3,2,4,7,0,3,5,4,3,6,6,3,2,7,8,9,8,7,7,2,1,2,1,7,7,2,7,4,5,9,5,6,3,1,6,6,1
%N A356092 Decimal expansion of the imaginary part of the first nontrivial zero of zeta'.
%C A356092 The nontrivial zero of zeta' with the smallest imaginary part is 2.4631618694543212... + i*23.2983204927628579...
%C A356092 The Riemann Hypothesis is equivalent to the assertion that zeta' has no nontrivial zero in the half-plane Re(z) < 1/2 (there are trivial zeros, e.g., -2.717262829204574...).
%H A356092 Benoit Cloitre, <a href="/A356092/a356092.png">Picture of some nontrivial zeros of zeta'</a>.
%H A356092 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>.
%t A356092 RealDigits[Im[x /. FindRoot[Derivative[1][Zeta][x], {x, 2 + 23*I}, WorkingPrecision -> 100]]][[1]] (* _Amiram Eldar_, Aug 14 2022 *)
%Y A356092 Cf. A356216.
%K A356092 nonn,cons
%O A356092 2,1
%A A356092 _Benoit Cloitre_, Aug 13 2022