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arXiv · 1809.03134

The error term in the prime number theorem

Dave Platt·Tim Trudgian
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Abstract

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.

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Dave Platt, Tim Trudgian. 2018-09-10. The error term in the prime number theorem. https://arxiv.org/abs/1809.03134

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