On arithmetic structures in dense sets of integers

By Ben Joseph Green. 2002

60 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/774f0711793eec74f443eaf6ed3b23704b02ec75

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

In Discrete Mathematics and Combinatorics

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

In Geometry and Topology

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

Citations in the corpus

• New bounds for Szemeredi's theorem, II: A new bound for r_4(N) (2006, methodology): “An exponent N − 1 /C d may be obtained by the simpler device of iteratively applying the case d = 1 of Proposition A.2 (see [6] for details), but this does not suffice for our purposes here.”
• The primes contain arbitrarily long polynomial progressions (2006, methodology): “However in 2004, Green and Tao [18] discovered a transference principle which allowed one (at least in principle) to reduce questions about configurations in special sets of zero density (such as the primes P :={2, 3, 5, 7, ... }) to questions about sets of positive density in the integers.”