Sharp forms of Nevanlinna error terms in differential equations

Details Sharp forms of Nevanlinna error terms in differential equations Sharp forms of Nevanlinna error terms in differential equations

2006-08-21

arxiv.org/abs/math/0608514v1

Symposium on Complex Differential and Functional Equations, 117 - 133, Univ. Joensuu Dept. Math. Rep. Ser., 6, Univ. Joensuu,

Mathematics

Complex Variables

16 pages, contains an erratum at the end of the paper

Scientific paper

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.

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