Lelechenko A. Arithmetic functions associated with exponential divisors

The thesis is devoted to the exponential divisor function and its generalizations. For the first time the algorithm for optimization of the rational objective function over exponent pairs under linear constraints is obtained. We improve the result of Tao, Croot and Helfgott on the parity of number of primes in the interval. The exponential divisor function is generalized on Gaussian integers; its statistical properties are studied in details. We improve asymptotic estimates of the functions, associated with semiproper exponential divisors. We also obtain the result on distribution of values of the Carmichael function over squarefree numbers and its exponential analog over k-full numbers.