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Additive problems with some conditions. (English. Russian original) Zbl 0838.11061

Lith. Math. J. 33, No. 2, 108-113 (1993); translation from Liet. Mat. Rink. 33, No. 2, 142-148 (1993).
In dealing with asymptotics for the sum \(\sum_{n \leq x} f(n) \cdot d_k (n) \cdot r(n - 1)\), where \(d_k (n)\) is the number of distinct representations of \(n\) by \(k\) divisors, \(r(n)\) is the number of representations of \(n\) as the sum of two squares, and \(|f(n) |\leq 1\), problems of probabilistic number theory are solved. In particular, necessary and sufficient conditions are found for the weak convergence of some sequences of distribution functions to a limit distribution function.

MSC:

11N37 Asymptotic results on arithmetic functions
11K65 Arithmetic functions in probabilistic number theory
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References:

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