We make explicit a theorem of Pintz concerning the error term in the prime number theorem. This gives an improved version of the prime number theorem with error term roughly square-root of that which was previously known. We apply this to a long-standing problem concerning an inequality studied by Ramanujan.

中文翻译：

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素数定理中的误差项

我们明确了关于质数定理中误差项的 Pintz 定理。这给出了质数定理的改进版本，其误差项大致是先前已知的误差项的平方根。我们将此应用于有关拉马努金研究的不等式的长期问题。