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

Massias, Jean-Pierre; Robin, Guy

J. Théor. Nombres Bordx. 8, No. 1, 215-242 (1996).

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.

Reviewer: W.E.Briggs (Boulder)

MSC:

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

Keywords:

effective bounds; primes; sums of primes

References:

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