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A356216 Decimal expansion of the real part of the first nontrivial zero of zeta'. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,cons
AUTHOR
Benoit Cloitre, Aug 13 2022
STATUS
approved

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Last modified April 10 17:05 EDT 2024. Contains 371607 sequences. (Running on oeis4.)