Some Applications

Abstract

The emphasis of this book is Nevanlinna’s Second Main Theorem, and the precise structure of its error term; applications of the Second Main Theorem, or of Nevanlinna theory more generally, are not our focus. However, for the student just learning Nevanlinna theory, we feel we must provide some sort of survey of what Nevanlinna theory is “good for” so to speak, and this is what we aim to do in the present chapter. Our goal here is to describe a variety of applications in as little space as possible, not to present the most current or refined application of any given type. Indeed, many of the applications we give here are due to R. Nevanlinna himself, and Nevanlinna’s own 1929 monograph [Nev(R) 1929] is one place the reader can find more refined versions and more detailed exploration of some of the applications we present here. We have, however, also made some limited effort to direct the interested reader to some of the current literature related to the applications discussed here.