Projective metric number theory

Author:

Ghosh Anish,Haynes Alan

Abstract

AbstractIn this paper we consider the probabilistic theory of Diophantine approximation in projective space over a completion of ℚ. Using the projective metric studied in [Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 23 (1996), no. 2, 211–248] 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.

Funder

EPSRC

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Upper bounds and spectrum for approximation exponents for subspaces ofn;Journal de théorie des nombres de Bordeaux;2023-01-27

2. Badly approximable points for diagonal approximation in solenoids;Acta Arithmetica;2021

3. A class of maximally singular sets for rational approximation;International Journal of Number Theory;2020-06-16

4. A note on badly approximabe sets in projective space;Mathematische Zeitschrift;2016-05-30

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