Sharp forms of Nevanlinna error terms in differential equations

Abstract

Sharp versions of some classical results in differential equations are given. Main results consists of a Clunie and a Mohon'ko type theorems, both with sharp forms of error terms. The sharpness of these results is discussed and some applications to nonlinear differential equations are given in the conluding remarks. Moreover, a short introduction on the connection between Nevanlinna theory and number theory, as well as on their relation to differential equations, is given. In addition, a brief review on the recent developments in the field of sharp error term analysis is presented.