The mean values of multiplicative functions. II

The mean values of multiplicative functions. IV.

“…In this paper we continue the investigations of publications [6], [7], [8], [9]. Let G(n) = G(n; g 1 , .…”

“…It is easy to apply our Theorem to the functions from a set G (for the definition of G see [8]). For example, let…”

Poisson Distribution for a Sum of Additive Functions

“…Finally the estimate (16) and the relation (15) show that the distributions (1) converge weakly to the Poisson law with the parameter λ. Theorem 3 is proved.…”

“…From his result the central limit theorem for the difference of consecutive values of some additive function follows. More general results were later established by Kubilius [8], Kátai [7], Hildebrand [6], Elliott [1][2][3][4], Timofeev and Usmanov [18], Stepanauskas [14][15][16][17], etc. In these works, the class of additive functions was expanded.…”

The mean-value of a product of shifted multiplicative functions and the average number of points of elliptic curves

“…A lot of work has been done to find the asymptotic behavior of M x,h (F, G) under various conditions, (see for example [17], [12], [18], [19], [5], [20]). In many of those cases, the functions are required to be close to 1 on the set of primes.…”