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180bc03 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | import OAI.NumberTheory.TwoPoint.ShortIntervals.MRTInputsTheorem
import OAI.NumberTheory.TwoPoint.MainWithMRTInputs
namespace OAI
/-! Paper 009-01: the three original main results, unconditionally. -/
namespace TwoPointCorrelations
/-- Theorem 1.1: ordinary Liouville correlations with an absolute logarithmic saving. -/
theorem liouvilleLogSaving : LiouvilleLogSaving :=
liouvilleLogSaving_of_mrt mrtLiouvilleShortInput
/-- Theorem 1.2: the binary corrected Elliott theorem. -/
theorem binaryCorrectedElliott : BinaryCorrectedElliott :=
binaryCorrectedElliott_of_mrt mrtShortExponentialInput
/-- Corollary 1.3: the corrected Elliott theorem for nonproportional affine forms. -/
theorem affineCorrectedElliott : AffineCorrectedElliott :=
affineCorrectedElliott_of_mrt mrtShortExponentialInput
end TwoPointCorrelations
end OAI
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