Respondent

Stasiv Nadiya Yuriivna

Theme

Asymptotic properties of random Dirichlet series

Defence Date

27.06.2019

Annotation

The dissertation consists of an introduction, 3 chapters, conclusions to each section and general conclusions,
list of sources used. The introduction substantiates the relevance of the research topic, formulates the purpose,
task, subject, object and methods of the research, presents the scientific novelty, the practical significance of the
results obtained, the relationship of work with scientific themes and the personal contributions of the author ofthe dissertation, a list of conferences and scientific seminars, on which the results of the dissertation research are
tested; List of publications in which the main results of the dissertation are published.
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 coeffi-
cients 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.
Keywords: random Dirichlet series, multiple Dirichlet series, abscissa of convergence, R-order of the growth,
entire function.

Dissertation File

Autosummary File