Effective bounds for certain functions concerning prime numbers
type: Item
instance of: scholarly article
title: Effective bounds for certain functions concerning prime numbers
zbMATH Open document ID: 0856.11043
author: Jean-Pierre Massias
author: Guy Robin
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1997-02-23T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/227434
full work available at URL: jtnb8-1.html
review text: Let \(p_k\) be the \(k\)-th prime number and let \(\theta(p_k)= \sum^k_{i=1}\log p_i\). The authors obtain new estimates and improvements of the bounds given by Rosser and Schoenfeld, Schoenfeld, and Robin for the functions \(p_k\), \(\theta(p_k)\), \(S_k= \sum^k_{i=1}p_i\) and \(S(\chi)=\sum_{p\leq x}p\). The estimates are obtained by using methods based on the Stieltjes integral and by direct calculation for small values.
Mathematics Subject Classification ID: 11N25
Mathematics Subject Classification ID: 11N56
zbMATH DE Number: 912508
zbMATH Keywords: effective bounds
zbMATH Keywords: primes
zbMATH Keywords: sums of primes
reviewed by: W. E. Briggs
MaRDI profile type: Publication
OpenAlex ID: W2029896593
cites work: Majoration explicite de l'ordre maximum d'un élément du groupe symétrique
cites work: Évaluation asymptotique de l'ordre maximum d'un élément du groupe symétrique
cites work: Effective Bounds for the Maximal Order of an Element in the Symmetric Group
cites work: Estimates for the Chebyshev Function ψ(x) - θ(x)
cites work: 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
cites work: Q3801652
cites work: Approximate formulas for some functions of prime numbers
cites work: Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)
cites work: Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
cites work: Deterministic one-counter automata
cites work: Q4045670
DOI: 10.5802/JTNB.166
Recommended article: Explicit Bounds for Some Functions of Prime Numbers
Recommended article: Improved explicit bounds for some functions of prime numbers
Recommended article: New bounds for the prime counting function
Recommended article: Explicit estimates of some functions over primes
Recommended article: Q4923659
Recommended article: New estimates for some functions defined over primes
Recommended article: A lower bound for the prime counting function
Recommended article: Explicit bounds for primes in arithmetic progressions
Recommended article: Q4885308
description: scientific article; zbMATH DE number 912508