We study Dirichlet series convergent only in a half-plane and whose sequence of exponents can be extended to some "regular" sequence. We establish the best possible k-order estimates for the sum of the Dirichlet series in the half-strip whose width depends on a special distribution density of the exponents.
We study Dirichlet series converging only in a half-plane such that their sequence of exponents admits an extension to a "regular" sequence. We prove the exactness of two-sided estimates for-order of the sum of the Dirichlet series in a semi-strip whose width depends on the special distribution density of the exponents.
We study the class of entire functions represented by Dirichlet series with real coefficients determined by a convex growth majorant. We prove the criterion for the validity of an asymptotic identity on the positive ray which is an exact estimate for the growth of the logarithm of the modulus for each function in the considered class.
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