C = ?
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Tomasz Ordowski
May 19, 2026, 3:15:05 AMMay 19
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Hello!
As is well known,
Sum_{n=2..oo} (zeta(n)-1) = 1.
How to prove that
C = Integral_{x=1+gamma..oo} (zeta(x)-1)dx < 1 ?
It seems that C = 0.9992286...
I expected exactly C = 1.
What do you think?
Best,
Tom Ordo
______________________
(but that is not exactly C either).
Tomasz Ordowski
May 19, 2026, 6:20:17 AMMay 19
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PS. Amiram Eldar noticed that the constant
C = Sum_{n>=2} 1/(n^(1+gamma)*log(n)) =
Integral_{x=1+gamma..oo} (zeta(x)-1)dx =
0.9992286... Is this equivalent for sure?
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