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On Ramanujan's prime counting inequality

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Publication:5881606
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DOI10.7153/mia-2022-25-71OpenAlexW4312264998MaRDI QIDQ5881606

Christian Axler

Publication date: 13 March 2023

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.02486


zbMATH Keywords

Riemann hypothesisprime counting functionRamanujan's prime counting inequality


Mathematics Subject Classification ID

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


Related Items

Sharper bounds for the error term in the prime number theorem



Cites Work

  • Unnamed Item
  • Unnamed Item
  • On an inequality of Ramanujan concerning the prime counting function
  • Improving bounds on prime counting functions by partial verification of the Riemann hypothesis
  • Remarks on Ramanujan's inequality concerning the prime counting function
  • On Solving a Curious Inequality of Ramanujan
  • An analytic method for bounding 𝜓(𝑥)
  • The error term in the prime number theorem
  • Estimates for $\pi(x)$ for large values of $x$ and Ramanujan's prime counting inequality
  • Updating the error term in the prime number theorem
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