On the error term in the explicit formula of Riemann-von Mangoldt II

2024/02/01 by Johnston, Daniel R., Cully-Hugill, Michaela · 3 citations
#11M26 (Primary) 11N05 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.04272

Abstract

We give an explicit O(x/T) error term for the truncated Riemann--von Mangoldt explicit formula. For large x, this provides a modest improvement over previous work, which we demonstrate via an application to a result on primes between consecutive powers.

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