An Improvement to Zaremba’s Conjecture

By ShinnYih Huang. 2013

61 citations recorded by the source corpus.

We prove there exists a density one subset $${\mathfrak{D} \subset \mathbb{N}}$$D⊂N such that each $${n {\in} {\mathfrak{D}}}$$n∈D is the denominator of a finite continued fraction with partial quotients bounded by 5.

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

View Paper: https://www.semanticscholar.org/paper/646cad848c0c8ef49f0c2ffa8f7db75148af64bf

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In Algebra and Number Theory

1. Alex Kontorovich
2. Jean Bourgain
3. H. Oh
4. Peter Sarnak
5. P. P. Varj'u
6. A. Mohammadi
7. Ilya D. Shkredov
8. Harald Andrés Helfgott

In Discrete Mathematics and Combinatorics

1. Alex Kontorovich
2. Jean Bourgain
3. H. Oh
4. P. P. Varj'u
5. Ilya D. Shkredov
6. Tom Sanders
7. Peter Sarnak
8. Moubariz Z. Garaev

In Mathematical Physics

1. Alex Kontorovich
2. Jean Bourgain
3. Peter Sarnak
4. H. Oh
5. P. P. Varj'u
6. Larry Guth
7. Massimiliano Berti
8. A. Mohammadi

Citations in the corpus

• Zaremba’s conjecture (2011, methodology): “Specifically, in the (homogeneous) linear congruential 2http://arxiv.org/abs/1107.3776v1 3Added in press: Huang [Hua13] has combined the methods of Frolenkov-Kan with ours to obtain the full density one statement with δ0 = 5/6.”