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

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

Table of n, a(n) for n=2..128.

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

Cf. A356216.

Sequence in context: A299619 A215269 A352485 * A359427 A336246 A351251

Adjacent sequences: A356089 A356090 A356091 * A356093 A356094 A356095

Keyword

nonn,cons

Author

Benoit Cloitre, Aug 13 2022

Status

approved