OAI/NumberTheory/TwoPoint/Halasz/HalaszStationaryPhase.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Locate the unique possible stationary point and quantify the slope away from it on a positive finite interval.

  1. lemma OAI.TwoPointCorrelations.halasz_log_slope_drop line 13
  2. lemma OAI.TwoPointCorrelations.halasz_log_stationary_center line 24
  3. theorem OAI.TwoPointCorrelations.halasz_log_stationary_integral line 58

    Source documentation

    Uniform square-root cancellation for an individual Poisson integral.

    theorem halasz_log_stationary_integral (u v a b : ℝ) (hu : 0 < u)
        (ha : 0 < a) (hab : a ≤ b) :
        ‖∫ x in a..b, halaszLogPhase u v x‖ ≤ 10*b/Real.sqrt u := by
    …

    Mentions: OAI.TwoPointCorrelations.halaszLogPhase