A still sharper region where $\pi (x)-{\mathrm {li}}(x)$ is positive

DOI10.1090/S0025-5718-2015-02930-5zbMath1323.11063OpenAlexW1507390359MaRDI QIDQ5264134

Patrick Demichel, Yannick Saouter, Timothy S. Trudgian

Publication date: 20 July 2015

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2015-02930-5

zbMATH Keywords

logarithmic integralRiemann zeta-functionprime counting functionSkewes' number

Mathematics Subject Classification ID

Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Software, source code, etc. for problems pertaining to number theory (11-04) Power residues, reciprocity (11A15) Primality (11Y11) Analytic computations (11Y35)

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Uses Software

• Maple

Cites Work

• The prime-counting function and its analytic approximations. \(\pi(x)\) and its approximations
• A sharp region where 𝜋(𝑥)-𝑙𝑖(𝑥) is positive
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• Computing $\pi (x)$ analytically
• An improved upper bound for the argument of the Riemann zeta-function on the critical line
• On the difference π(x) - li(x)