Improving bounds on prime counting functions by partial verification of the Riemann hypothesis

DOI10.1007/s11139-022-00616-xOpenAlexW3196476086WikidataQ114223553 ScholiaQ114223553MaRDI QIDQ2097526

Daniel R. Johnston

Publication date: 14 November 2022

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.02249

zbMATH Keywords

Riemann zeta-functionRiemann hypothesisprime counting functionRamanujan inequality

Mathematics Subject Classification ID

Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Distribution of primes (11N05) Values of arithmetic functions; tables (11Y70)

Related Items

On Ramanujan's prime counting inequality ⋮ An explicit upper bound for \(L(1,\chi)\) when \(\chi\) is quadratic ⋮ Sharper bounds for the error term in the prime number theorem ⋮ On the error term in the explicit formula of Riemann–von Mangoldt ⋮ Sharper bounds for the Chebyshev function \(\psi(x)\) ⋮ Some explicit estimates for the error term in the prime number theorem ⋮ New bounds for numbers of primes in element orders of finite groups

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