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2 days ago comment added Zhobbyist Fair catch. $C_k$ does depend on $s_0$ and the relation is only valid in the $s$ neighborhood of $s_0$. I've edited the question to make that clear.
2 days ago history edited Zhobbyist CC BY-SA 4.0
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2 days ago comment added Stopple You displayed equation is not precise enough to say anything. The left side depends on $k$, the right does not (or only implicitly $C=C_k$). The right side depends on $s_0$, the left does not. What happens if $s_0$ is replaced with another zeta zero $s_0^\prime$? How can the left be $\approx$ both?
Dec 8 at 12:58 history edited YCor CC BY-SA 4.0
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S Dec 8 at 6:50 review First questions
Dec 8 at 7:31
S Dec 8 at 6:50 history asked Zhobbyist CC BY-SA 4.0