On the local-global conjecture for integral Apollonian gaskets

By Jean Bourgain, Alex Kontorovich. 2012

64 citations recorded by the source corpus.

We prove that a set of density one satisfies the local-global conjecture for integral Apollonian gaskets. That is, for a fixed integral, primitive Apollonian gasket, almost every (in the sense of density) admissible (passing local obstructions) integer is the curvature of some circle in the gasket.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/092d537611208be310abbc251177644ede560654

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. A. Mohammadi
2. H. Oh

In Discrete Mathematics and Combinatorics

1. A. Mohammadi
2. H. Oh
3. Harald Andrés Helfgott
4. Alexander Gorodnik
5. Akshay Venkatesh

In Mathematical Physics

1. A. Mohammadi
2. H. Oh
3. Peter Sarnak
4. Alexander Gorodnik
5. Akshay Venkatesh
6. Y. Benoist
7. Gregory Margulis
8. Alex Kontorovich

Citations in the corpus

• Matrix coefficients, counting and primes for orbits of geometrically finite groups (2012, methodology): “We also formulate our counting statements for bisectors in the HAK decomposition, motivated by recent applications in [7] and [8].”
• Random walks in compact groups (2012, unknown): “Let c1, α, β and A be positive numbers satisfying β α and A ≥ (α− β)−1 − 1.”