{
  "id": "irrationality-of-special-values",
  "title": "Irrationality of special values",
  "description": "Irrationality proofs by small linear forms and by determinants. The irrationality of ζ(2) and Apéry's theorem that ζ(3) is irrational, by Beukers' integrals and an involution of the unit interval; then the complete proof that Catalan's constant G = 1 - 1/9 + 1/25 - ... is irrational: determinants of mixed moments with Chebyshev rows whose Taylor contact cancels ζ(2), lower bounds for their denominators at the prime 2 and at the odd primes by base-p digit reductions, nonvanishing at prime scales by Frobenius and a finite certificate, and an upper bound at the real place by an integral formula, bounded interpolation, Chebyshev expansions of logarithmic kernels and an exact root certificate.",
  "units": [
    {
      "id": "small-linear-forms-and-aperys-theorem",
      "title": "Small linear forms and Apéry's theorem",
      "reader": "small-linear-forms-and-aperys-theorem.html",
      "source": "src/small-linear-forms-and-aperys-theorem.md",
      "source_sha256": "a833da7675bcafe01e2bd2b5986f13d78d0324cadfe370e48658d4cafe0db362",
      "status": "author_self_checked"
    },
    {
      "id": "chebyshev-rows-and-mixed-moments",
      "title": "Chebyshev rows and mixed moments",
      "reader": "chebyshev-rows-and-mixed-moments.html",
      "source": "src/chebyshev-rows-and-mixed-moments.md",
      "source_sha256": "c1cadda23ddbb8972f7bcc0c26408abc0f70fbea47b1e13258b1c156f6d84d89",
      "status": "author_self_checked"
    },
    {
      "id": "denominators-at-the-prime-two",
      "title": "Denominators at the prime two",
      "reader": "denominators-at-the-prime-two.html",
      "source": "src/denominators-at-the-prime-two.md",
      "source_sha256": "b02f24e5fda2e7379c2789b43f93a6c4c5a1aa244a0faae605451267b3c3ba66",
      "status": "author_self_checked"
    },
    {
      "id": "denominators-at-the-odd-primes",
      "title": "Denominators at the odd primes",
      "reader": "denominators-at-the-odd-primes.html",
      "source": "src/denominators-at-the-odd-primes.md",
      "source_sha256": "6213004198abef2e5c68ccb7088f550f21893fbc2cc5c6a986ac4312c50606b9",
      "status": "author_self_checked"
    },
    {
      "id": "nonvanishing-at-prime-scales",
      "title": "Nonvanishing at prime scales",
      "reader": "nonvanishing-at-prime-scales.html",
      "source": "src/nonvanishing-at-prime-scales.md",
      "source_sha256": "53af4be636e92342dd394b7a4d17e7bc615e18de5c830850274e2c3739a4a1eb",
      "status": "author_self_checked"
    },
    {
      "id": "the-real-place-integral-formula-and-two-bounds",
      "title": "The real place: integral formula and two bounds",
      "reader": "the-real-place-integral-formula-and-two-bounds.html",
      "source": "src/the-real-place-integral-formula-and-two-bounds.md",
      "source_sha256": "109ba5d9bb509af9c50be1e1d570b546381a408ca701c65b86ca4e689b55d173",
      "status": "author_self_checked"
    },
    {
      "id": "the-energy-bound-and-the-irrationality-of-catalans-constant",
      "title": "The energy bound and the irrationality of Catalan's constant",
      "reader": "the-energy-bound-and-the-irrationality-of-catalans-constant.html",
      "source": "src/the-energy-bound-and-the-irrationality-of-catalans-constant.md",
      "source_sha256": "0fe4e57dd45d77d21a846d85cd0ff0f3222164d63e6c4debfcbb3f33d06dc0a7",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [
    "Core course D10 (measure and integration: monotone convergence, Fubini's theorem)",
    "Core course C50 (complex analysis: Cauchy's integral formula, maximum modulus principle)",
    "NT-ZETA lesson on the prime number theorem (Theorem 3.1)",
    "NT-LOC lesson on completions and the p-adic numbers"
  ],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}