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AlexKontorovich committed Jan 29, 2024
1 parent 53b8548 commit 0b21e79
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1 change: 0 additions & 1 deletion PrimeNumberTheoremAnd/HoffsteinLockhart.lean
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Expand Up @@ -58,7 +58,6 @@ $$
-\frac{\zeta'}{\zeta}(\sigma+it) \ll (\log t)^2
$$
there.
$$
\end{theorem}
\begin{proof}
\uses{thm:Fsigma'}
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2 changes: 1 addition & 1 deletion PrimeNumberTheoremAnd/MellinCalculus.lean
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Expand Up @@ -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)|
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