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.
Higher Correlations of Divisor Sums Related to Primes II: Variations of the error term in the prime number theorem
On Littlewood's proof of the prime number theorem
On the properties of generalized harmonic and oscillatory numbers. Simple proof of the Prime Number Theorem
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