New bounds for the prime counting function π(x)

2014/09/05 by Christian Axler, Axler, Christian
Mathematics · #11A41 #11B05 #11N05 #Advanced Mathematical Identities #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1409.1780

openalex publication_date 2014/09/05 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper we establish a number of new estimates concerning the prime counting function π(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in small intervals.

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