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. 
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78 Citations
Highly Influential Citations
3
Background Citations
24
Methods Citations
7
Results Citations
1

78 Citations

Multiplier ideal sheaves, Nevanlinna theory, and Diophantine approximation
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
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
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
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
  • H. Pastén
  • Mathematics
    Mathematical 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
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
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…
Powerful values of polynomials and a conjecture of Vojta
A generalized subspace theorem for closed subschemes in subgeneral position.
On the arithmetic case of Vojta's conjecture with truncated counting functions
. 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…
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References

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Diophantine approximations and foliations
In this paper we indicate the proof of an effective version of the Green-Griffiths conjecture for surfaces of general type and positive second Segre class (i.e.c12>c2). Naturally this effective…
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Nevanlinna Theory and Its Relation to Diophantine Approximation
Nevanlinna Theory for Meromorphic Functions and Roth's Theorem Holomorphic Curves into Compact Riemann Surfaces and Theorems of Siegel, Roth, and Faltings Holomorphic Curves in Pn(C) and Schmidt's…
Diophantine Approximations and Diophantine Equations
Siegel's lemma and heights.- Diophantine approximation.- The thue equation.- S-unit equations and hyperelliptic equations.- Diophantine equations in more than two variables.
Algebro-geometric version of Nevanlinna’s lemma on logarithmic derivative and applications
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…
On Galois Extensions of a Maximal Cyclotomic Field
This paper is devoted to the realization of certain types of Chevalley groups as the Galois group of extensions of certain cyclotomic fields. In addition, a criterion for an algebraic curve to be…
Topics in Nevanlinna theory
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Mumford's Degree of Contact and Diophantine Approximations
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
Contents: Heights - Nomalized heights - The Mordell-Weil theorem - Mordell's conjecture - Local calculation of normalized heights - Siegel's method - Baker's method - Hilbert's irreducibility theorem…
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