Diophantine Approximation and Nevanlinna Theory
@inproceedings{Vojta2011DiophantineAA, title={Diophantine Approximation and Nevanlinna Theory}, author={Paul Vojta}, year={2011} }
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.
78 Citations
Multiplier ideal sheaves, Nevanlinna theory, and Diophantine approximation
- Mathematics
- 2012
This paper states a conjecture for Nevanlinna theory or diophantine approximation, with a sheaf of ideals in place of the normal crossings divisor. This is done by using a correction term involving a…
Greatest common divisors of analytic functions and Nevanlinna theory on algebraic tori
- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2019
Abstract We study upper bounds for the counting function of common zeros of two meromorphic functions in various contexts. The proofs and results are inspired by recent work involving greatest common…
Birational Nevanlinna constants, beta constants, and diophantine approximation to closed subschemes
- Mathematics
- 2020
In an earlier paper (joint with Min Ru), we proved a result on diophantine approximation to Cartier divisors, extending a 2011 result of P. Autissier. This was recently extended to certain closed…
On the conjectures of Vojta and Campana over function fields with explicit exceptional sets
- Mathematics
- 2022
We prove new cases of Vojta’s conjectures for surfaces in the context of function fields, with truncation equal to one and providing an effective explicit description of the exceptional set. We also…
Bounded ranks and Diophantine error terms
- MathematicsMathematical Research Letters
- 2019
We show that Lang's conjecture on error terms in Diophantine approximation implies Honda's conjecture on ranks of elliptic curves over number fields. We also show that even a very weak version of…
Divisibility of polynomials and degeneracy of integral points
- Mathematics
- 2021
We prove several statements about arithmetic hyperbolicity of certain blow-up varieties. As a corollary we obtain multiple examples of simply connected quasi-projective varieties that are…
Kobayashi Hyperbolicity and Higher-dimensional Nevanlinna Theory
- Mathematics
- 2015
This note is a survey concerning Kobayashi hyperbolicity problem and higher dimensional Nevanlinna theory. The central topic of this note is a famous open problem to characterize which projective…
On the arithmetic case of Vojta's conjecture with truncated counting functions
- Mathematics
- 2022
. We prove a Diophantine approximation inequality for rational points in varieties of any dimension, in the direction of Vojta’s conjecture with truncated counting functions. Our results also provide…
References
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Abstract In this paper we shall establish some generalization of Nevanlinna’s Lemma on Logarithmic Derivative to the case of meromorphic maps from a finite analytic covering space over the…
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The purpose of this note is to present a somewhat unexpected relation between diophantine approximations and the geometric invariant theory. The link is given by Mumford's degree of contact. We show…
Lectures On The Mordell-Weil Theorem
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