Updating the error term in the prime number theorem

DOI10.1007/s11139-014-9656-6zbMath1398.11123arXiv1401.2689OpenAlexW1978559180MaRDI QIDQ5963785

Tim Trudgian

Publication date: 23 February 2016

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

Full work available at URL: https://arxiv.org/abs/1401.2689

zbMATH Keywords

prime number theoremChebyshev functionsRamanujan's inequality

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Distribution of primes (11N05)

Related Items (22)

On Ramanujan's prime counting inequality ⋮ Explicit zero density for the Riemann zeta function ⋮ EXPLICIT ZERO‐FREE REGIONS FOR DIRICHLET ‐FUNCTIONS ⋮ Improved explicit bounds for some functions of prime numbers ⋮ On the First <em>k</em>-Ramanujan Prime ⋮ Remarks on Ramanujan's inequality concerning the prime counting function ⋮ Sharper bounds for the error term in the prime number theorem ⋮ Sharper bounds for the Chebyshev function \(\psi(x)\) ⋮ Some explicit estimates for the error term in the prime number theorem ⋮ On the counting function of semiprimes ⋮ Global numerical bounds for the number-theoretic omega functions ⋮ Explicit estimates of some functions over primes ⋮ Constrained ternary integers ⋮ The error term in the prime number theorem ⋮ An explicit result for primes between cubes ⋮ Primes between consecutive powers ⋮ On the first sign change of $\theta (x) -x$ ⋮ New estimates for some functions defined over primes ⋮ Estimates for $\pi(x)$ for large values of $x$ and Ramanujan's prime counting inequality ⋮ Sharper bounds for the Chebyshev function 𝜃(𝑥) ⋮ Variants on Andrica's conjecture with and without the Riemann hypothesis ⋮ On the regularity of primes in arithmetic progressions

Cites Work

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• On Solving a Curious Inequality of Ramanujan
• On a conjecture of Pomerance
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)
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• VINOGRADOV'S INTEGRAL AND BOUNDS FOR THE RIEMANN ZETA FUNCTION
• A Strong Form of a Problem of R. L. Graham
• Primes in arithmetic progressions
• New bounds for $\psi (x)$
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• Une région explicite sans zéros pour la fonction ζ de Riemann

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