Episode 78 · The Machine's Theorems
Primes and Zeros: The Quasi-Riemann Hypothesis
Zeta and Dirichlet L-functions built from scratch; why zeros control prime counts; the classical sliver and Siegel zeros; Theorem 1.1 of the 199-page manuscript and its Lean scope; the proof architecture over the Eisenstein integers; how referees will check it; the human-assisted 11/12 companion and the 9-page Siegel-zero paper; least nonresidues, deterministic square roots and Scholze's crypto worry; Artin, Catalan, prime gaps and Chowla. Keywords: Riemann zeta, quasi-Riemann hypothesis, zero-free region, Dirichlet L-functions, Siegel zeros, Hecke L-functions, cubic theta, large sieve, Vinogradov, Artin primitive root, Catalan's constant, Chowla, Lean
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Inside this episode
- Cold open: the grant and the half-plane
- A sum, a product, and the primes
- Riemann's eight pages
- Why zeros count primes
- A tiny example: primes ending in one, three, seven and nine
- A sliver near the line: what was known before
- The claim, exactly
- Inside the hundred and ninety-nine pages
- How a proof like this gets checked
- The companions: eleven-twelfths, and nine pages on Siegel zeros
- Square roots, nonresidues, and Scholze's worry
- The neighbours: Artin, Catalan, prime gaps and Chowla
- What it would mean, what is still open, and the ledger
Production credits & AI disclosure
Scripts generated with Claude Opus. Synthetic narration generated with Edge TTS. Reviewed, listened to, and approved by Sankalp Thakur.