The Error Term In The Primes Counting Function

Details The Error Term In The Primes Counting Function The Error Term In The Primes Counting Function

2009-08-11

arxiv.org/abs/0908.1546v1

Mathematics

General Mathematics

14 Pages

Scientific paper

This article considers the error term of the primes counting function. It
applies some recent results on the densities of prime numbers in short
intervals to derive an improvement of the error term from subexponential size
to fractional exponential size. The corresponding equivalent results for the
zeros of the zeta function and Mertens conjecture are also discussed.

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