Stasyuk Y. Asymptotic relations for functions analytic in the half-plane

It is established that the description of the value of the exceptional set in the analogues of Erdos-Macintyre theorems cannot be improved. New unimprovable conditions sufficient for the asymptotic equality of sum and maximal term of the Dirichlet series with nonmonotonous exponents to carry are found. For functions analytic in a strip the final variant of the Wiman type theorem is obtained. A new description of exceptional sets in the Wiman-Valiron type theorems for functions analytic in strips and disc are found. A new description of exceptional set in asymptotic relations for the Dirichlet series absolutely convergent in the halfplane and the logarithmic derivative of its maximum modulus is obtained.