Information on the thesis

In the thesis the lower and the upper estimates of the sum of Dirichlet series
with arbitrary abscissa of absolute convergence and positive coefficients are obtained.
These estimates are applied to establishing the connecting between the growth loga-
rithm of maximum modulus and maximal term in the terms of comparison functions.
It was possible to establish the connection between the growth of maximum
modulus and maximum term and the behaviour of the coefficients of the Dirichlet
series with null abscissa of absolute convergence in the terms of many-termed power
asymptotics. The analogues of Lindel¨of’s theorem and Whittaker’s inequality for
the Dirichlet series absolutely convergent in the halfplane of the finite R-order by
Gaisin are obtained.
Key words: Dirichlet series, maximum modulus, maximal term, many-termed
power asymptotics, R-order, abscissa of absolute convergence.