Abstract:
Summation of multiplicative functions is found in almost half of the problems of analytical number theory. The central place in the question of summing the values of multiplicative functions is occupied by questions about the asymptotic behavior of sums of the form $$ m(X)=\sum_{n\leq X}f(n), $$ for $X\rightarrow\infty$, where $f(n)$ is a multiplicative function of a natural argument. This article is devoted to the study of summation of multiplicative functions over numbers whose prime divisors lie in specified intervals. An asymptotic formula is obtained for the sums of the product of multiplicative functions whose prime divisors lie in specified intervals.
Keywords:asymptotics, sum of products of multiplicative functions, prime divisors, given intervals, natural argument, integral equations, generalized Mangoldt function, prime numbers, complex numbers, sieve method.
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