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

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, 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, 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

Offset

1,1

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' (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...).

Links

Table of n, a(n) for n=1..127.

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.

Example

2.463161869454321285874395053306329144920793134567323475022217370727117508671...

Mathematica

RealDigits[Re[x /. FindRoot[Derivative[1][Zeta][x], {x, 2 + 23*I}, WorkingPrecision -> 100]]][[1]] (* Amiram Eldar, Aug 14 2022 *)

Crossrefs

Cf. A356092.

Sequence in context: A085593 A220336 A021410 * A336843 A061504 A077179

Adjacent sequences: A356213 A356214 A356215 * A356217 A356218 A356219

Keyword

nonn,cons

Author

Benoit Cloitre, Aug 13 2022

Status

approved