Arithmetic Progressions in Sets of Fractional Dimension

By I. Łaba, M. Pramanik. 2007

131 citations recorded by the source corpus.

Let $${E \subset\mathbb{R}}$$ be a closed set of Hausdorff dimension α. Weprove that if α is sufficiently close to 1, and if E supports a probability measure obeying appropriate dimensionality and Fourier decay conditions, then E contains non-trivial 3-term arithmetic progressions.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b9ecba213e81fc484be18e42f0236b30483d5d21

How researchers see this paper

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In Discrete Mathematics and Combinatorics

1. I. Łaba
2. Vincent Chan
3. M. Pramanik

In Geometry and Topology

1. I. Łaba
2. Vincent Chan
3. M. Pramanik

In Mathematical Physics

1. I. Łaba
2. M. Pramanik
3. Máté Matolcsi
4. Terence Tao

Citations in the corpus

• Finite configurations in sparse sets (2013, background): “While in [25] this proof could be reused almost verbatim, more substantial changes are needed in the multidimensional case.”