OAI/NumberTheory/TwoPoint/Halasz/HalaszConstantGrowth.lean

GitHub source file

4 declarations, 0 contain sorry, 0 declared as axioms

Polynomial-in-the-degree control of the logarithm of the explicit iteration constant. The absolute prime-supply threshold is retained.

  1. lemma OAI.TwoPointCorrelations.four_terms line 9
  2. lemma OAI.TwoPointCorrelations.halasz_iteration_threshold_growth line 16
  3. lemma OAI.TwoPointCorrelations.halasz_iteration_base_growth line 51
  4. theorem OAI.TwoPointCorrelations.halasz_selected_constant_growth line 100

    Source documentation

    The constant at the selected moment has logarithm O(k^4 log k). No endpoint-dependent constant is hidden.

    theorem halasz_selected_constant_growth {R₀ k : ℕ} (hk : 2≤k) :
        halaszIterationConstant R₀ k (10*k)≤(R₀+k+32)^(256*k^4) := by
    …

    Mentions: OAI.TwoPointCorrelations.halaszIterationConstant