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Reciprocal sums of a class of additive functions in short intervals

Reciprocal sums of a class of additive functions in short intervals
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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)≥t<sub>0</sub>】0 (n≥2) and f(p)≡1 and obtained an asymptotic formula, where t<sub>0</sub> 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),
出处 《Chinese Science Bulletin》 SCIE EI CAS 1997年第2期102-105,共4页
关键词 ADDITIVE functions RIEMANN ZETA-FUNCTION ASYMPTOTIC formula. additive functions Riemann zeta-function asymptotic formula
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