Reciprocal sums of a class of additive functions in short intervals  

作　　者：ZHAI WenguangDepartment of Mathematics, Shandong Normal University, Jinan 250014, China 

出　　处：《Chinese Science Bulletin》1997年第2期102-105,共4页

摘　　要：USING the method of probabilistic number-theory, De Koninck, and De Koninck and Galambos studied the reciprocal sum of the additive function f（n） satisfying f（n）≥t₀】0 （n≥2） and f（p）≡1 and obtained an asymptotic formula, where t₀ is an absolute positive constant. Let B（x） denote the number of n≤x not satisfying the inequality loglogn-R（x）≤f（n）≤loglogn+R（x）, （1） where R（x） is a function tending to infinity. Then in refs. [1, 2], it is proved that if R（x）=o（loglogx） and B（x）=o（x/loglogx）,

关 键 词：ADDITIVE functions RIEMANN ZETA-FUNCTION ASYMPTOTIC formula. 

分 类 号：O174[理学—数学]