OAI/NumberTheory/Ostmann/Arithmetic/ArithmeticTwoPrimePatternNormRate.lean

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The full numerical norm bound with the original equality patterns

  1. theorem OAI.Ostmann.arithmetic_two_prime_pattern_norm_rate line 15

    Source documentation

    The actual pattern sum and paired frequency sum have an absolute bulk constant. The cutoff includes the constructed bottom reserve 2 sqrt(m). Only the genuine comparison errors use the full number of histories.

    theorem arithmetic_two_prime_pattern_norm_rate (ψ : SchwartzMap ℝ ℂ) (n k : ℕ)
        (hk : 0 < k) (hn : n ≤ k) (B Cfreq Cprior ε : ℝ)
        (hCfreq : 0 ≤ Cfreq) (hCprior : 1 ≤ Cprior) (hε : 0 < ε)
        (hdepth : 8 * (Cprior + 1) ≤ (k : ℝ) ^ 3) :
        ∀ᶠ L : ℝ in atTop, let m := spectatorBulkCount k L
    …

    Mentions: OAI.Ostmann.spectatorBulkCount

  2. theorem OAI.Ostmann.arithmetic_two_prime_original_pattern_norm_rate line 94

    Source documentation

    The actual pattern sum and paired frequency sum have an absolute bulk constant. The cutoff includes the constructed bottom reserve 2 sqrt(m). The fifth error is the literal giant comparison; only comparison errors use the full number of histories.

    theorem arithmetic_two_prime_original_pattern_norm_rate (ψ : SchwartzMap ℝ ℂ) (n k : ℕ)
        (hk : 0 < k) (hn : n ≤ k) (B Cfreq Cprior ε : ℝ)
        (hCfreq : 0 ≤ Cfreq) (hCprior : 1 ≤ Cprior) (hε : 0 < ε)
        (hdepth : 8 * (Cprior + 1) ≤ (k : ℝ) ^ 3) :
        ∀ᶠ L : ℝ in atTop, let m := spectatorBulkCount k L
    …

    Mentions: OAI.Ostmann.spectatorBulkCount