Value distribution theory of Nevanlinna

Abstract

In the field of research, a century old value distribution theory of Nevanlinna is still alive. It contains a broad range of implementations inside and outside a function theory. It is the study to speculate different values by complex function. As you are aware that each single non-constant variable polynomial upon ℂ has has not more than one root which is complex. This builds polynomials with real coefficients, because upon seeing the real number as a complex number with its imaginary part equal to zero up to constant multiple. This article express mainly the classical version for complex analytic map to the Riemann sphere of single variable, with priority on mero-morphic functions in the z-plane.