explicit-formula

Weil's explicit formula for ζ(s): an exact magic function F = Ξ²H shows the Odlyzko–Poitou–Serre method is sharp for ζ (κ* ≤ 0), and every positive solution is ζ's own zeros and primes (Conjectures S and U of Part I). Paper, certificates, Lean 4 spine and reviewing guide.

Open, reproducible research on the Riemann hypothesis with explicit evidence states, negative results, and formal-verification plans.

N-zero explicit formula approximation study: numerical analysis of ψ(x) and consistency with the Riemann Hypothesis

Draft (unpublished): exact explicit-formula verification of the function-field Legendre conjecture for d <= 10, fluctuations of prime counts, and a characteristic-2 anomaly.

27 windows onto Riemann's zeros — another way to see them. Not a proof; honest pedagogy, checked against 2000 real zeros.

Positive solutions of Weil's explicit formula for ζ(s): uniqueness near ζ's own zeros and primes, and certificates showing the optimal explicit-formula conductor bound reaches 1 − 8.98·10⁻¹⁰⁶⁰ (κ* ≤ 1.43·10⁻¹⁰⁶⁰). Conjectures S and U are proved in Part II (nic410/zeta-sharpness-uniqueness). Paper, companion works and verification records.

Numerical lab for the zeros↔primes coupling on GL(1) L-functions (Riemann ζ, Dirichlet L): the Weil positivity functional and the multiplicativity residual, measured on the same objects. Measurement, not proof — no RH/GRH claim.