Named afterFinnishmathematicianRolf Nevanlinna (1895–1980), who published the theory in 1925.[1]
Nevanlinnatheory (uncountable)
- (complex analysis) A part of the theory ofmeromorphicfunctions that describes theasymptoticdistribution of solutions to the equation ƒ(z) =a, asa varies.
A key tool inNevanlinna theory is the Nevanlinna characteristic,
, which measures the rate of growth of a meromorphic function.
1992, Ilpo Laine,Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter,page 1:Precisely, our aim has been to show how theNevanlinna theory may be applied to get insight into the properties of solutions of complex differential equations.
2001, William Cherry, Zhuan Ye,Nevanlinna's Theory of Value Distribution, Springer,page vi:Motivated by an analogy betweenNevanlinna theory and Diophantine approximation theory, discovered independently by C. F. Osgood [Osg 1985] and P. Vojta [Vojt 1987], S. Lang recognized that the careful study of the error term in Nevanlinna'a Second Main Theorem would be of interest in itself.
- 2010,Paul Vojta,Diophantine Approximation andNevanlinna theory, Jean-Louis Colliot-Thélène, Peter Swinnerton-Dyer, Paul Vojta (editors),Arithmetic Geometry: Lectures given at the C.I.M.E. Summer School, Springer,Lecture Notes in Mathematics 2009,page 111,
- Beginning with the work of Osgood [65], it has been known that the branch of complex analysis known asNevanlinna theory (also calledvalue distribution theory) has many similarities with Roth's theorem on diophantine approximation.[…]The circle of ideas has developed further in the last 20 years: Lang's conjecture on sharpening the error term in Roth's was carried over to a conjecture inNevanlinna theory which was proved in many cases.
part of the theory of meromorphic functions
