🌀 Today’s dive into ζ′/ζ
Spent the morning peeling back another layer of the zeta function. Turns out: if you zoom in on height t, only the zeros ρ with ∣𝑡ᵨ−𝑡∣≤1 really matter (𝐼𝑚(ρ)=𝑡ᵨ) — everything else dissolves into a clean O(log⁡∣t∣) haze.
It’s wild how much structure hides behind a single identity: \( \frac{\zeta'(s)}{\zeta(s)}
= -\frac{1}{s-1}
+ \sum_{\rho:\, |t_\rho - t|\le 1} \frac{1}{s-\rho}
+ O(\log(|t|+4)). \)
Not easy stuff, but exactly the kind of scaffolding we can build on top of The Riemann Hypothesis Revealed. Every step makes the landscape a little less mysterious.
Onward.
🔗https://cortexdrifter.blogspot.com/2026/04/a-small-taste-from-my-new-book-season-2.html

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The Riemann hypothesis, explained by Jørgen Veisdal: 🔗 https://www.cantorsparadise.com/the-riemann-hypothesis-explained-fa01c1f75d3f
\[\boxed{\zeta(s)=0,\ s\notin2\mathbb{Z}^-\implies\Re(s)=\dfrac{1}{2}}\]

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The #Search for #SiegelZeros - #Numberphile

https://www.youtube.com/watch?v=Bn946gIck3g&ab_channel=Numberphile

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