On close-to-pseudoconvex Dirichlet series - O. M. Mulyava; M. M. Sheremeta; M.G. Medvediev (Математичні Студії)
For a Dirichlet series of form $F(s)=\exp\{sλ_1\}+\sum\nolimits_{k=2}^{+∞}f_k\exp\{sλ_k\}$ absolutely convergent in the half-plane $Π_0=\{s\colon \mathop{\rm Re}s<0\}$ new sufficient conditions for the close-to-pseudoconvexity are found and the obtained result is applied to studying of solutions linear differential equations of second order with exponential coefficients. In particular, are proved the following statements: