# Applications of Diophantine Approximation to Integral Points and Transcendence

@inproceedings{Corvaja2018ApplicationsOD, title={Applications of Diophantine Approximation to Integral Points and Transcendence}, author={Pietro Corvaja and Umberto Zannier}, year={2018} }

Diophantine approximation may be roughly described as the branch of number theory concerned with approximations by rational numbers; or rather, this constituted the original motivation. That such questions have attracted continued attention is undoubtedly substantially due to their relevance for another, more ancient, topic: the theory of Diophantine equations, namely those whose solutions have to be found in integers or rationals, possibly in a finite extension of Q. The connections between…

## 14 Citations

### HYPERBOLICITY OF VARIETIES OF LOG GENERAL TYPE KENNETH ASCHER AND AMOS TURCHET

- Mathematics
- 2020

Diophantine Geometry aims to describe the sets of rational and/or integral points on a variety. More precisely one would like geometric conditions on a variety X that determine the distribution of…

### Bounded Generation by semi-simple elements: quantitative results

- Mathematics
- 2022

We prove that for a number field F , the distribution of the points of a set Σ ⊂ AnF with a purely exponential parametrization, for example a set of matrices boundedly generated by semi-simple…

### Some arithmetical properties of convergents to algebraic numbers

- Mathematics
- 2022

. Let ξ be an irrational algebraic real number and ( p k /q k ) k ≥ 1 denote the sequence of its convergents. Let ( u n ) n ≥ 1 be a non-degenerate linear recurrence sequence of integers, which is…

### On the dth Roots of Exponential Polynomials and Related Problems Arising from the Green–Griffiths–Lang Conjecture

- MathematicsThe Journal of Geometric Analysis
- 2020

We show that if an exponential polynomial $$\sum _{i=1}^m P_i(z)e^{Q_i(z)}$$ ∑ i = 1 m P i ( z ) e Q i ( z ) , where $$P_i$$ P i , $$Q_i\in \mathbb C[z]$$ Q i ∈ C [ z ] , is a d th power, $$d\ge 2$$…

### The Lang–Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties

- Mathematics
- 2020

These notes grew out of a mini-course given from May 13th to May 17th at UQAM in Montreal during a workshop on Diophantine Approximation and Value Distribution Theory. We start with an overview of…

### The Hilbert Property for integral points of affine smooth cubic surfaces

- MathematicsJournal of Number Theory
- 2019

### THE DYNAMICAL MORDELL–LANG CONJECTURE FOR ENDOMORPHISMS OF SEMIABELIAN VARIETIES DEFINED OVER FIELDS OF POSITIVE CHARACTERISTIC

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2019

Abstract Let $K$ be an algebraically closed field of prime characteristic $p$, let $X$ be a semiabelian variety defined over a finite subfield of $K$, let $\unicode[STIX]{x1D6F7}:X\longrightarrow X$…

### Around the Chevalley–Weil theorem

- Mathematics
- 2022

We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also…

### Non-virtually abelian anisotropic linear groups are not boundedly generated

- MathematicsInventiones mathematicae
- 2021

We prove that if a linear group $$\Gamma \subset \mathrm {GL}_n(K)$$ Γ ⊂ GL n ( K ) over a field K of characteristic zero is boundedly generated by semi-simple (diagonalizable) elements then it is…

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