Updating the error term in the prime number theorem

Trudgian, Tim S.

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Updating the error term in the prime number theorem

Date

2015-01-08

Authors

Trudgian, Tim S.

Publisher

Springer Verlag (Germany)

Abstract

An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, the third to a conjecture by Pomerance and the fourth to an inequality studied by Ramanujan.