login
A356092
Decimal expansion of the imaginary part of the first nontrivial zero of zeta'.
2
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, 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, 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
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
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
Cf. A356216.
Sequence in context: A299619 A215269 A352485 * A359427 A336246 A351251
KEYWORD
nonn,cons
AUTHOR
Benoit Cloitre, Aug 13 2022
STATUS
approved