New bounds for $\psi (x)$

DOI10.1090/S0025-5718-2014-02886-XzbMath1310.11085arXiv1310.6374MaRDI QIDQ5179226

Laura Faber, Habiba Kadiri

Publication date: 19 March 2015

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

Full work available at URL: https://arxiv.org/abs/1310.6374

zbMATH Keywords

prime number theoremexplicit formulazeros of Riemann zeta function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (19)

An explicit density estimate for Dirichlet $L$-series ⋮ Explicit zero density for the Riemann zeta function ⋮ EXPLICIT ZERO‐FREE REGIONS FOR DIRICHLET ‐FUNCTIONS ⋮ Explicit estimates for the distribution of numbers free of large prime factors ⋮ Counting zeros of the Riemann zeta function ⋮ Some explicit estimates for the error term in the prime number theorem ⋮ Explicit estimates of some functions over primes ⋮ Corrigendum to New bounds for $\psi (x)$ ⋮ Solution of the minimum modulus problem for covering systems ⋮ An analytic method for bounding 𝜓(𝑥) ⋮ Estimates of $\psi ,\theta $ for large values of $x$ without the Riemann hypothesis ⋮ On the first sign change of $\theta (x) -x$ ⋮ Updating the error term in the prime number theorem ⋮ Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function ⋮ Estimating $\pi (x)$ and related functions under partial RH assumptions ⋮ Explicit average orders: news and problems ⋮ Unnamed Item ⋮ Sharper bounds for the Chebyshev function 𝜃(𝑥) ⋮ Mean values of long Dirichlet polynomials with higher divisor coefficients

Uses Software

• SumTools
• ZetaGrid

Cites Work

• On the roots of the Riemann zeta-function
• Short effective intervals containing primes
• Approximate formulas for some functions of prime numbers
• A zero density result for the Riemann zeta function
• Every odd number greater than $1$ is the sum of at most five primes
• Extended computation of the Riemann zeta‐function
• On the Zeros of the Riemann Zeta Function in the Critical Strip. IV
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)
• Primes in arithmetic progressions
• Explicit estimates for the summatory function of \varLambda (n)ń from the one of \varLambda (n)
• Computing $\pi (x)$ analytically
• Une région explicite sans zéros pour la fonction ζ de Riemann
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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