Dirichlet series and power series: solutions of algebric differential equations

Abstract

In this thesis, we consider two classes of algebraic di erential equations, namely, linear di erential equations and generalized Riccati di erential equations. We are interested in certain properties of the coe cients and exponents of their solutions. For Dirichlet series solutions, we give the pattern of its coe cients and exponents. For Power series solutions, we provide the bound of its coe cients.