Documentation

MathlibNt.SieveTheory.LiLiuGoldbachB10IntegralScalarUpper

theorem MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachB10SiftedCount_540996_upper (δ : ℝ) (hδ : 0 < δ) :
∃ (B : ℝ), 0 ≤ B ∧ ∀ (ε : ℝ), 0 < ε → ε < 1 → ∃ (N₀ : ℕ), 4 ≤ N₀ ∧ ∀ (N : ℕ), N₀ ≤ N → Even N → have Δ := ↑N ^ (1 / 2) / Real.log ↑N ^ (B + 1); have Z := Δ ^ (1 / 2); ↑(goldbachB10SiftedCount N ε (↑N ^ goldbachB10Beta) (↑N ^ goldbachB10Gamma) Z) ≤ (540996 / 100000 * (1 - ε) + δ) * (SingularSeries.liuSingularSeries N * ↑N / Real.log ↑N ^ 2)

Actual B10SiftedCount at the unchanged legal cutoff, retaining (1-ε). This statement concerns neither an original G10 count nor a corrected G10 count.

Inspect dependencies

MathlibNt.SieveTheory.LiLiuOnePlusOneNine.GoldbachBig.goldbachB10SiftedCount_540996_upper · compiled type and proof/definition references.