OAI/NumberTheory/TotientAsymptotic/PrimeNumberTheorem.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

Discharge of the ordinary PNT input using the pinned library's proved Wiener--Ikehara theorem and Mathlib's Chebyshev comparison formulas.

  1. lemma OAI.TotientAsymptotic.psi_nat_ratio_tendsto line 14
  2. lemma OAI.TotientAsymptotic.psi_real_ratio_tendsto line 32
  3. lemma OAI.TotientAsymptotic.theta_real_ratio_tendsto line 46
  4. lemma OAI.TotientAsymptotic.prime_counting_ratio_tendsto line 65
  5. theorem OAI.TotientAsymptotic.primeNumberTheoremInput line 78

    Source documentation

    The PNT hypothesis in every conditional main theorem is now proved.

    theorem primeNumberTheoremInput : PrimeNumberTheoremInput := by
…

    Mentions: OAI.TotientAsymptotic.PrimeNumberTheoremInput