# Projective metric number theory

@article{Ghosh2011ProjectiveMN, title={Projective metric number theory}, author={Anish Ghosh and Alan Haynes}, journal={arXiv: Number Theory}, year={2011} }

In this paper we consider the probabilistic theory of Diophantine approximation in projective space over a completion of Q. Using the projective metric studied by Bombieri, van der Poorten, and Vaaler we prove the analogue of Khintchine's Theorem in projective space. For finite places and in higher dimension, we are able to completely remove the condition of monotonicity and establish the analogue of the Duffin-Schaeffer conjecture.

## 3 Citations

### Badly approximable points for diagonal approximation in solenoids

- MathematicsActa Arithmetica
- 2021

In this paper we investigate the problem of how well points in finite dimensional p-adic solenoids can be approximated by rationals. The setting we work in was previously studied by Palmer, who…

### A note on badly approximabe sets in projective space

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Recently, Ghosh and Haynes (J Reine Angew Math 712:39–50, 2016) proved a Khintchine-type result for the problem of Diophantine approximation in certain projective spaces. In this note we complement…

### Topics in homogeneous dynamics and number theory

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This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.

### A class of maximally singular sets for rational approximation

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We say that a subset of [Formula: see text] is maximally singular if its contains points with [Formula: see text]-linearly independent homogenous coordinates whose uniform exponent of simultaneous…

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