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{c}

The classical zero-free region and a truncated Perron contour give
$$
\sum_{n\leq x}\Lambda(n)
=x+O\left(xe^{-c\sqrt{\log x}}\right)
$$
for some constant $c>0$.


Prime number theorem with classical zero-free-region error

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 150 / 2 / b / Solution

Prime number theorem with classical zero-free-region error

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Prime number theorem with classical zero-free-region error

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