Riemann hypothesis and some new integrals connected with the integral negativity of the remainder in the formula for the prime-counting function π(x)

2011/05/25 by Jan Moser, Moser, Jan
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #advanced mathematical theories #math.CA

paper · pdf · doi:10.48550/arxiv.1105.4945

arxiv created 2011/05/25 · openalex publication_date 2011/05/25 · arxiv updated 2011/05/26 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper a new integral for the remainder of π(x) is obtained. It is proved that there is an infinite set of the formulae containing miscellaneous parts of this integral.

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