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We consider a method for estimating asymptotics of arithmetic functions on aarithmetic progression in the paper. This question is closely related with thedistribution of primes. Problems often arise even with the definition ofasymptotic of the mean value of arithmetic functions, and even more with thedetermination of asymptotics of moments of higher orders. Therefore, the paperproposes (a different from the traditional) probabilistic approach based on thelimiting distribution of arithmetic functions on an arithmetic progression. Weconsider arithmetic functions with limiting normal distribution. Severalassertions are proved about the estimation of asymptotics of moments ofstrongly additive arithmetic functions on a arithmetic progression, as well asadditive functions of the class and arithmetic functions of the class havingthe same limit distribution. Versions 1 and 2 consider the asymptotics of themoments of arithmetic functions with normal limit distribution in naturalseries.

Estimate of asymptotics of moments of arithmetic functions defined on an arithmetic progression and having a limit - normal distribution