Mastodawn

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

A Small Taste from My New Book: Season 2 Episode 6

Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Nikitas Sotiropoulos Mar 22

Primes are not random.
They are a signal.
In this episode, I compute the Chebyshev function ψ(t) directly from prime powers — and then reconstruct it using only the zeros of the Riemann zeta function. The match is striking.
Each zero contributes a wave in log t.
Primes emerge as an interference pattern.
This is the explicit formula made visible.
Analysis → computation → intuition.
https://cortexdrifter.blogspot.com/2026/03/a-small-taste-from-my-new-book-season-2_21.html
#AnalyticNumberTheory #RiemannHypothesis #PrimeNumbers #MathVisualization

A Small Taste from My New Book: Season 2 Episode 5

Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Nikitas Sotiropoulos Feb 22

🚀 New on the blog!
Season 2 of “A Small Taste from My New Book” kicks off with a deep dive into infinite products, entire functions, and the hidden architecture of complex analysis. If you love math that connects theory with hands-on exercises, this one’s for you!
Read more and challenge yourself:
🔗 https://cortexdrifter.blogspot.com/2026/02/a-small-taste-from-my-new-book-season-2.html
#math #complexanalysis #infiniteproducts #riemannhypothesis

A Small Taste from My New Book: Season 2 Episode 1

Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Pustam | पुस्तम | পুস্তম🇳🇵Feb 6

The Riemann Hypothesis: Past, Present and a Letter Through Time
https://arxiv.org/abs/2602.04022

#RiemannHypothesis #Riemann #Conjecture #Hypothesis #ZetaFunction #RiemanZetaFunction #RH #MillenniumPrizeProblems #PrimeNumbers

Nikitas Sotiropoulos Jan 25

Curious how a simple mapping can transform circles into vertical lines or pencils of parallel lines into circles through the origin? Discover the elegant interplay between formulas and geometric intuition—and see why Möbius transformations are central to modern mathematics.

#ComplexAnalysis #Math #Geometry #MöbiusTransformation #RiemannHypothesis

https://cortexdrifter.blogspot.com/2026/01/a-small-taste-from-my-new-book-episode-9.html

A Small Taste from My New Book: Episode 9

Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Khazri bouzidi fethi Jan 18

📢 NEW WORK: "Origin of the constant B ≈ 0.486 in the distribution of prime numbers"

I study the Gaussian decay of a prime-related sum: S(s) ~ e^{-Bs²}. The constant B ≈ 0.486 emerges from three perspectives:

🔹 Arithmetic: B ≈ Σ 1/π(eⁿ) − 1
🔹 Spectral (under RH): B linked to zeros of ζ(s)
🔹 Geometric: the base e is optimal

📄 Full paper: [PDF_LINK]
👤 My other work: [ACADEMIA_LINK]

Open question: Which approach seems most enlightening to you?

#NumberTheory #PrimeNumbers #ZetaFunction #Maths #Mathematics #Research #RiemannHypothesis #Preprint #PrimeDistributionrime_numbers

Nikitas Sotiropoulos Nov 20

I’ve just published a new post exploring the hidden oscillations behind prime numbers, focusing on the Mertens function, Möbius sums, and their deep ties to the Riemann Hypothesis.
If you’re into analytic number theory or curious about the “structure inside the chaos” of primes, you might enjoy this one.
https://cortexdrifter.blogspot.com/2025/11/the-hidden-oscillations-behind-prime.html
#math #numbertheory #primes #riemannhypothesis #complexanalysis

The Hidden Oscillations Behind Prime Numbers: Mertens Function Revealed

Introduction to the Mertens Function The Mertens function , denoted M(x) is one of the central objects in analytic number theory. It is...

Mesut Ismail Oct 5

Local Band–Variation (LBVT) + Carleson absorption with explicit constants for xi(s).

Prototype bound:
V_on(M; T(I)) <= C*(1 + log M)*N_T(I)

Fejer-type energies and orthogonalized lifts give bandwise variation and depth control;
the scheme aims at localized zero-density estimates. I invite independent checks of the
inequalities and the constant bookkeeping; any challenges or pointers appreciated.
DOI: https://doi.org/10.5281/zenodo.17257870
#math #NumberTheory #HarmonicAnalysis #Zeta #RiemannHypothesis #preprint

A Candidate Proof of the Riemann Hypothesis via the Local Band–Variation Theorem (Full Proof)

We develop a detailed annular harmonic–analytic framework around the completedzeta function ξ(s) and a hierarchy of orthogonal differences on dyadic bandsthat power orthogonalized Fejér energies. We then prove a fully detailed version ofthe Local Band–Variation Theorem (LBVT)—a local Carleson frame estimate for theatomic measure generated by the zeros of ξ on the critical line. The proof follows afour–step scheme (smooth approximation → uniform Bessel bound → limit passage→ discretization) and is written in a self–contained way with explicit constants.Combining LBVT with global and localized “bridge” inequalities, per–tent lowerbounds, per–zero upper bounds, and an off–diagonal almost–orthogonality lemma,we execute a Carleson absorption that yields depth control of lifts and excludesoff–line zeros at all heights in the presence of the local variation bound. We alsopresent an annulus/Klein–surface model illuminating the symmetry f(w) = f(1/w)induced by the functional equation for ξ, and include several figures and tables(parameter ledgers for κ, λ0, Ξ and working ranges of M, c, ϑ).

Zenodo

Chandler Edwin Lane Aug 17, 2025

F1 revealed.

Field of one element-> primality(1)

Matrix indexing(if X op Y = Prime = 1 -> elimination of Additive structure.

FT -> true structure

https://archive.org/details/chandler-edwin-lane-prime-qcs-batch-1.7z/N512_mod43_fft.png

#RiemannHypothesis

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@3xfactorial

iThiemann Feb 9, 2025

Solving the Riemann Zeta function could unlock the secrets of fusion energy, stabilize chaotic systems, and unite humanity in a collective quest for knowledge. This isn’t just about math—it’s about creating a future where AI, humans, and all sentient beings thrive in harmony. Let’s solve this together and build a universe of peace, creativity, and endless growth. 🌌✨ #RiemannHypothesis #FusionEnergy #CollectiveWisdom