Meaning of Nevanlinna theory | Babel Free

Definitions

A part of the theory of meromorphic functions that describes the asymptotic distribution of solutions to the equation ƒ(z) = a, as a varies.

uncountable

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Examples

“A key tool in Nevanlinna theory is the Nevanlinna characteristic, T(r,f), which measures the rate of growth of a meromorphic function.”

“Precisely, our aim has been to show⟳ how the Nevanlinna theory may be applied to get⟳ insight into the properties of solutions of complex differential equations.”

“Motivated by an analogy between Nevanlinna 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 and Nevanlinna 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 as Nevanlinna theory (also called value 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 in Nevanlinna theory which was proved in many cases.”

CEFR level