An Asymptotic Expansion

Volume 4, Issue 2, 2003

Article 30

AN ASYMPTOTIC EXPANSION

UNIVERSITATEA BUCURESTI
FACULTATEA DE MATEMATICA
STR. ACADEMIEI NR. 14, RO-70109,
BUCURESTI, ROMANIA.
E-Mail: gamin@al.math.unibuc.ro

Received 24 December, 2002; Accepted 12 May, 2003.
Communicated by: L.Tóth

ABSTRACT. In this paper we study the asymptotic behaviour of the sequence $% \left(r_n\right)_n$ of the powers of primes. Calculations also yield the evaluation $\sqrt{r_n}-p_n=o\left(\frac{n}{\mathnormal{log}^sn}\right)$ for every positive integer s,

denoting the

-th prime.

Key words:
Powers of primes, Inequalities, Asymptotic behaviour.

2000 Mathematics Subject Classification:
11N05, 11N37

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