The prime-counting function and its analytic approximations. \(\pi(x)\) and its approximations

DOI10.1007/s10444-007-9039-2zbMath1149.11004OpenAlexW2102814447WikidataQ56210595 ScholiaQ56210595MaRDI QIDQ937037

Tadej Kotnik

Publication date: 20 August 2008

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-007-9039-2

zbMATH Keywords

logarithmic integralprime-counting functionRiemann's approximation

Mathematics Subject Classification ID

Primes (11A41) Analytic computations (11Y35)

Related Items (12)

A sharp region where 𝜋(𝑥)-𝑙𝑖(𝑥) is positive ⋮ On a constant related to the prime counting function ⋮ Inequalities involving \(\pi (x)\) ⋮ A quantum model of the distribution of prime numbers and the Riemann hypothesis ⋮ Multidimensional scaling and visualization of patterns in prime numbers ⋮ On Euler products with smaller than one exponents ⋮ A NEW BOUND FOR THE SMALLEST x WITH π(x) > li(x) ⋮ Average prime-pair counting formula ⋮ On the first sign change of $\theta (x) -x$ ⋮ Updating the error term in the prime number theorem ⋮ The impact of 𝜁(𝑠) complex zeros on 𝜋(𝑥) for 𝑥<10^{10¹³} ⋮ A still sharper region where $\pi (x)-{\mathrm {li}}(x)$ is positive

Cites Work

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• Approximate formulas for some functions of prime numbers
• On the Difference π(x ) − lix (II)
• On the Sign of the Difference π(x) - li(x)
• Irregularities in the Distribution of Primes and Twin Primes
• VINOGRADOV'S INTEGRAL AND BOUNDS FOR THE RIEMANN ZETA FUNCTION
• A new bound for the smallest $x$ with $\pi(x) > \mathrm{li}(x)$
• On the difference π(x) - li(x)

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