diff --git a/PrimeNumberTheoremAnd/HoffsteinLockhart.lean b/PrimeNumberTheoremAnd/HoffsteinLockhart.lean index 34ff8040..564ddf10 100644 --- a/PrimeNumberTheoremAnd/HoffsteinLockhart.lean +++ b/PrimeNumberTheoremAnd/HoffsteinLockhart.lean @@ -58,7 +58,6 @@ $$ -\frac{\zeta'}{\zeta}(\sigma+it) \ll (\log t)^2 $$ there. -$$ \end{theorem} \begin{proof} \uses{thm:Fsigma'} diff --git a/PrimeNumberTheoremAnd/MellinCalculus.lean b/PrimeNumberTheoremAnd/MellinCalculus.lean index b579fd37..02991e47 100644 --- a/PrimeNumberTheoremAnd/MellinCalculus.lean +++ b/PrimeNumberTheoremAnd/MellinCalculus.lean @@ -104,7 +104,7 @@ lemma VerticalIntegral_Perron_le_one {x : ℝ} (xpos : 0 < x) (x_le_one : x < 1) · intro σ' σ'' σ'pos σ''pos have := rectIntLimit σ' σ'' σ'pos σ''pos sorry ---%% But we also have the bound $\int_{(\sigma')}\leq x^\sigma' * C$, where +--%% But we also have the bound $\int_{(\sigma')} \leq x^{\sigma'} * C$, where --%% $C=\int_\R\frac{1}{|(1+t)(1+t+1)|}dt$. have VertIntBound : ∃ C > 0, ∀ σ' > 1, Complex.abs (VerticalIntegral f σ') ≤ x^σ' * C · let C := ∫ (t : ℝ), 1 / |(1 + t) * (1 + t + 1)|