On a Generalization of Szemerédi's Theorem

By Ilya D. Shkredov. 2005

54 citations recorded by the source corpus.

Let N be a natural number and A ⊂ [1, …, N]2 be a set of cardinality at least N2/(loglog⁡N)c is an absolute constant. We prove that A contains a triple {(k, m), (k+d, m), (k, m+d)}, where d > 0. This theorem is a two‐dimensional generalization of Szemerédi's theorem on arithmetic progressions. 2000 Mathematics Subject Classification 35J25, 37A15.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/adba3e48a60e432cec255c2fac3f2bbcb67bf1c3

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In Algebra and Number Theory

1. Tom Sanders
2. Ben Joseph Green
3. Terence Tao
4. Nikos Frantzikinakis
5. Bryna Kra
6. T. Ziegler
7. William T. Gowers
8. B. Host

In Discrete Mathematics and Combinatorics

1. Tom Sanders
2. Ben Joseph Green
3. Terence Tao
4. William T. Gowers
5. Nikos Frantzikinakis
6. Bryna Kra
7. T. Ziegler
8. B. Host

In Geometry and Topology

1. Tom Sanders
2. Ben Joseph Green
3. Terence Tao
4. William T. Gowers
5. Nikos Frantzikinakis
6. Emmanuel Breuillard
7. B. Host
8. T. Ziegler

Citations in the corpus

• A quantitative version of the idempotent theorem in harmonic analysis (2006, methodology): “Since his work, similar ideas have been used in several places [8], [10], [13], [21], [22], [23].”