A242070 Decimal expansion of the supremum of all real s such that zeta'(s+i*t) = 0 for some real t.
2, 8, 1, 3, 0, 1, 4, 0, 2, 0, 2, 5, 2, 8, 9, 8, 3, 6, 7, 5, 2, 7, 2, 5, 5, 4, 0, 1, 2, 1, 6, 6, 8, 6, 9, 6, 3, 8, 4, 6, 1, 4, 0, 5, 6, 0, 5, 4, 0, 2, 6, 2, 2, 1, 5, 2, 6, 6, 4, 3, 8, 7, 4, 0, 4, 7, 1, 5, 0, 8, 3, 6, 8, 9, 2, 3, 7, 0, 7, 9, 9, 5, 8, 4, 0, 2, 0, 7, 1, 8, 2, 6, 3, 6, 9, 6, 0, 5, 4, 1
Offset: 1
Examples
2.81301402025289836752725540121668696384614056054026221526643874...
Links
- J. Arias de Reyna, J. van de Lune, Some bounds and limits in the theory of Riemann's zeta function. arXiv:1107.5134 [math.NT]
- Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 28.
Crossrefs
Cf. A242069.
Programs
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Mathematica
y /. FindRoot[Zeta'[y]/Zeta[y] == -2^(y + 1)*Log[2]/(4^y - 1), {y, 2}, WorkingPrecision -> 100] // RealDigits // First
Formula
The unique solution y > 1 of the equation zeta'(y)/zeta(y) = -2^(y + 1)*log(2)/(4^y - 1).