OAI/NumberTheory/Ostmann/Preliminaries/AdditiveSieveProof.lean

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The published additive large sieve, with its precise downstream constant

The finite cosecant Hilbert inequality and duality prove the separated-frequency estimate. Reduced fractions of denominator at most Q are 1/Q²-separated. This proves the specialization of Montgomery--Vaughan (1973), Theorem 1, used throughout the conditional development.

  1. abbrev OAI.Ostmann.ReducedFractionIndex line 18
  2. def OAI.Ostmann.reducedFractionPoint line 21
  3. theorem OAI.Ostmann.reducedFractionPoint_separated line 24
  4. theorem OAI.Ostmann.sieveAdditivePhase_eq_half line 42
  5. theorem OAI.Ostmann.reducedFraction_sum line 50
  6. theorem OAI.Ostmann.publishedAdditiveLargeSieve line 59