Projective metric number theory
-
Anish Ghosh
and
Alan Haynes
Abstract
In 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.
Funding source: EPSRC
Award Identifier / Grant number: EP/J00149X/1
Funding source: EPSRC
The first author thanks the ESI, Vienna for hospitality. The second author thanks Simon Kristensen for helpful conversations concerning the proof of Theorem 2.3. We thank the referees for helpful comments.
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Refined semiclassical asymptotics for fractional powers of the Laplace operator
- Projective metric number theory
- Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
- Right simple singularities in positive characteristic
- Discriminants and Artin conductors
- Hilbertian fields and Galois representations
- Simple endotrivial modules for quasi-simple groups
- A reconstruction theorem for abelian categories of twisted sheaves
- Hyperkähler manifolds of Jacobian type
- The algebra of essential relations on a finite set
Articles in the same Issue
- Frontmatter
- Refined semiclassical asymptotics for fractional powers of the Laplace operator
- Projective metric number theory
- Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
- Right simple singularities in positive characteristic
- Discriminants and Artin conductors
- Hilbertian fields and Galois representations
- Simple endotrivial modules for quasi-simple groups
- A reconstruction theorem for abelian categories of twisted sheaves
- Hyperkähler manifolds of Jacobian type
- The algebra of essential relations on a finite set
