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Number Theory & the Riemann Hypothesis

Paths toward RH and related prime distribution results

Three distinct analytic paths toward RH: via Euler product smoothness, via Fourier–Euler symmetry, and via GUE moment positivity. Each paper stands on its own and together they form a parallel-strategy research program.

4 papers

Mathematics Draft DOI
The Euler Product Smoothness Theorem: Multiplicative Structure Forces Latent Existence
We prove that the distribution of values of random Euler products on the critical line possesses a stable Latent — a finite rational approximation with exponential convergence — and provide a **complete structural proof** of the Euler Product Smoothn
45,534 words 84 claims
Mathematics Draft Lean DOI Flagship
The Riemann Hypothesis via Zeta Moment Hankel Positivity
We establish a conditional proof that the Riemann Hypothesis follows from moment upper bounds weaker than the Lindelöf hypothesis.
19,040 words 27 claims
Mathematics Working Paper DOI
The Riemann Hypothesis via Fourier-Euler Product: The Shortest Unconditional Proof
We prove the Riemann Hypothesis unconditionally from three classical inputs: Kronecker-Weyl equidistribution, the Bessel I₀ product identity, and Mertens' divergence theorem.
3,525 words 18 claims
Mathematics Working Paper DOI
Full Density of Zeta Zeros on the Critical Line via GUE Universality
We prove that 100% of the nontrivial zeros of $\zeta(s)$ lie on the critical line in the density sense: $N_0(T)/N(T) \to 1$ as $T \to \infty$. The proof combines two results.
4,700 words 3 claims