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p-adic Nevanlinna Theory outside of a hole

, 2017
Alain Escassut, Ta Thi Hoai An
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Positivity, hyperbolicity and Nevanlinna theory

Clara Dérand
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Nevanlinna theory and diophantine approximation [PDF]

Science in China Series A: Mathematics, 2005
We discuss the analogue of the Nevanlinna theory and the theory of Diophantine approximation, focussing on the second main theorem and abc-conjecture.
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A Modification of the Nevanlinna Theory

Computational Methods and Function Theory, 2009
We present a modification of the Nevanlinna theory which is inspired by previous work of H. Cartan and D. Drasin and which makes full use of Poisson-Jensen-Nevanlinna’s Formula. We show that the results from the “classical” Nevanlinna theory remain valid for this modification.
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Nevanlinna Theory of Functions

Nature, 1964
Meromorphic Functions By Prof. W. K. Hayman. (Oxford Mathematical Monographs.) Pp. xiv + 191. (London: Oxford University Press, 1964.) 63s.
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Brownian Motion and Nevanlinna Theory

Proceedings of the London Mathematical Society, 1986
The paper describes an interpretation of R. Nevanlinna's theory on the distribution of values taken by a meromorphic function in terms of probability theory. A meromorphic function transforms Brownian paths in its domain into Brownian paths on the Riemann sphere which run up to a stopping time T.
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Nevanlinna Theory and Diophantine Approximations

2004
In this note, we will introduce some basic problems and progresses in Nevanlinna theory and Diophantine approximations, say, discuss the abc-conjecture and Hall’s conjecture for integers, and prove their analogue for polynomials or entire functions by dint of Nevanlinna’s value distribution theory.
Hu, Pei-Chu, Yang, Chung-Chun
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Nevanlinna Theory in an Annulus

2006
A concrete presentation of Nevanlinna theory in a domain z: ¦z¦≥R has been offered by Bieberbach. He applied Green’s formula to prove the first main theorem and the lemma of the logarithmic derivative for meromorphic functions outside a disc of radius R.
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THE STRENGTH OF CARTAN'S VERSION OF NEVANLINNA THEORY

Bulletin of the London Mathematical Society, 2004
\textit{H. Cartan} proved a fundamental theorem in the value distribution theory [Sur les zeros des combinaisons linéaires de \(p\) functions holomorphes données', Mathematica Cluj 7, 5--31 (1933; Zbl 0007.41503)], which contains Nevanlinna's second main theorem.
Walter K. Hayman, Gary G. Gundersen
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