Effective bounds for certain functions concerning prime numbers. (Bornes effectives pour certaines fonctions concernant les nombres premiers.) (French) Zbl 0856.11043

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.


11N25 Distribution of integers with specified multiplicative constraints
11N56 Rate of growth of arithmetic functions
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