Stasiv N. Asymptotic properties of random Dirichlet series

In the dissertation, the main object of investigations are Dirichlet series with random exponents and random coefficients and also random multiple Dirichlet series. There were obtained the estimates of the abscissa of convergence of Dirichlet series with arbitrary sequence of positive exponents in terms of conditions imposed on the distribution functions of pairwise independent exponents of such series. The abscissas of convergence of random Dirichlet series with random exponents and random coefficients are investigated. In terms of restrictions imposed on the sequence of the distribution functions of pairwise independent exponents are established conditions in which the abscissa of absolute convergence almost surely (a.s.) is equal to the predetermined number or is infinite. Conditions in terms of the distribution functions of the sequence of random coefficients, in which R-types and R-orders of the growth of random Dirichlet series are equal to the predetermined nonnegative number or are infinities are given. For random multiple Dirichlet series in terms of the distribution functions of random coefficients, the domains of convergence are described and the relationship between them are established. The question of the description of R-orders of random Dirichlet series in terms of the distribution functions of the sequence of their random coefficients is investigated. All results of the thesis are new. They have theoretical meaning and can be used both in Dirichlet series theory and in the it’s applications.