| 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 | |