Discrete uniform limit law for additive functions

In the dissertation it is considered the weak convergence of the distributions of additive functions on shifted primes, of the sum of additive functions with shifted arguments and of the sum of additive functions on shifted primes to the discrete uniform law. The case when fx(p), x 2, take values 0 or 1 on primes is studied. The first chapter describes classical results and historical context of additive functions on shifted arguments. Other three chapters provides the sufficient and necessary conditions for a weak convergence of distributions of additive functions on shifted primes, of the sum of additive functions with shifted arguments and of the sum of additive functions on shifted primes to the discrete uniform law. The obtained results describe the limit behaviour of the sets of additive functions and can be applied in mathematical research that require knowledge of the asymptotic behaviour of the additive functions