The error term in the prime number theorem

Platt, David; Trudgian, Timothy

doi:10.1090/mcom/3583

The error term in the prime number theorem
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by David J. Platt and Timothy S. Trudgian HTML | PDF

Math. Comp. 90 (2021), 871-881 Request permission

Abstract:

We make explicit a theorem of Pintz, which gives a 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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