Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  061.07907
Autor:  Erdös, Pál
Title:  On some asymptotic formulas in the theory of the 'factorisatio numerorum'. (In English)
Source:  Ann. of Math., II. Ser. 42, 989-993 (1941); corrctions ibid. 44, 647-651 (1943).
Review:  Let 1 < a1 < a2 < ··· be a sequence of integers such that, for some \sigma, sumk = 1oo ak-\rho = 1 and sumk = 1oo log ak < oo, but not all ak are powers of a1. If l is a nonnegative integer and n is a positive integer, let Tl(n) be the coefficient of n in the Dirichlet series for (sumk = 1oo ak-\rho)l. Write f(n) = suml = 0oo Tl(n). It is proved in an elementary way that n-\rho summ = 1n f(m) has a positive limit as n ––> oo.
Classif.:  * 11N37 Asymptotic results on arithmetic functions
Index Words:  number theory

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