Nikitas Sotiropoulos🌀 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
Jensen’s formula as a microscope 🔍
By mixing geometry, analytic growth, and symmetry, we get tight control on local zero fluctuations in the critical strip—and a clean logarithmic bound emerges.
This is A Small Taste from My New Book — Season 2, Episode 6.
The machinery is set. Now let’s see what it reveals next.
🔗 https://cortexdrifter.blogspot.com/2026/03/a-small-taste-from-my-new-book-season-2_28.html
#RiemannHypothesis #AnalyticNumberTheory #MathBlog #JensensFormula
By mixing geometry, analytic growth, and symmetry, we get tight control on local zero fluctuations in the critical strip—and a clean logarithmic bound emerges.
This is A Small Taste from My New Book — Season 2, Episode 6.
The machinery is set. Now let’s see what it reveals next.
🔗 https://cortexdrifter.blogspot.com/2026/03/a-small-taste-from-my-new-book-season-2_28.html
#RiemannHypothesis #AnalyticNumberTheory #MathBlog #JensensFormula
Benjamin Leis ✅Carnival of Mathematics 210
https://aperiodical.com/2022/11/carnival-of-mathematics-210/
