Estimates of $\psi ,\theta $ for large values of $x$ without the Riemann hypothesis

DOI10.1090/mcom/3005zbMath1336.11069OpenAlexW2214854223MaRDI QIDQ2792347

Pierre Dusart

Publication date: 9 March 2016

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

Full work available at URL: https://doi.org/10.1090/mcom/3005

zbMATH Keywords

number theoryChebyshev functionsarithmetic functionserror term estimate

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Distribution of primes (11N05) Rate of growth of arithmetic functions (11N56)

Related Items (14)

Solving Program Sketches with Large Integer Values ⋮ EXPLICIT ZERO‐FREE REGIONS FOR DIRICHLET ‐FUNCTIONS ⋮ Improved explicit bounds for some functions of prime numbers ⋮ Sharper bounds for the error term in the prime number theorem ⋮ ON THE ITERATES OF THE SHIFTED EULER’S FUNCTION ⋮ Explicit estimates of some functions over primes ⋮ Corrigendum to New bounds for $\psi (x)$ ⋮ Difference bases in cyclic groups ⋮ Estimates of the \(k\)th prime under the Riemann hypothesis ⋮ The Riemann hypothesis in computer science ⋮ New estimates for some functions defined over primes ⋮ Estimates for $\pi(x)$ for large values of $x$ and Ramanujan's prime counting inequality ⋮ Unnamed Item ⋮ Sharper bounds for the Chebyshev function 𝜃(𝑥)

Uses Software

• ZetaGrid

Cites Work

• Unnamed Item
• Unnamed Item
• Maximal product of primes whose sum is bounded
• Sieving the positive integers by large primes
• Prime numbers and computer methods for factorization.
• An improved upper bound for the argument of the Riemann zeta-function on the critical line. II
• Approximate formulas for some functions of prime numbers
• Every odd number greater than $1$ is the sum of at most five primes
• Small values of the Euler function and the Riemann hypothesis
• Estimation de la fonction de Tchebychef θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• Primes in arithmetic progressions
• Explicit estimates for the summatory function of \varLambda (n)ń from the one of \varLambda (n)
• New bounds for $\psi (x)$
• Computing $\pi (x)$ analytically
• Une région explicite sans zéros pour la fonction ζ de Riemann
• Values of the Euler 𝜙-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields
• Explicit Bounds for Some Functions of Prime Numbers

This page was built for publication: Estimates of $\psi ,\theta $ for large values of $x$ without the Riemann hypothesis