OFFSET
2,1
COMMENTS
The nontrivial zero of zeta' with the smallest imaginary part is 2.4631618694543212... + i*23.2983204927628579...
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...).
LINKS
Benoit Cloitre, Picture of some nontrivial zeros of zeta'.
Norman Levinson and Hugh L. Montgomery, Zeros of the derivatives of the Riemann zeta-function, Acta Mathematica, Vol. 133 (1974), pp. 49-65; alternative link.
MATHEMATICA
RealDigits[Im[x /. FindRoot[Derivative[1][Zeta][x], {x, 2 + 23*I}, WorkingPrecision -> 100]]][[1]] (* Amiram Eldar, Aug 14 2022 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Benoit Cloitre, Aug 13 2022
STATUS
approved