Additive Combinatorics: Long arithmetic progressions in sum sets

By Terence Tao, V. Vu. 2006

788 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0d981678cb76a6de0ffc495efef04391d39c6c52

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

An introduction to large deviations for random graphs (2016, background): “An excellent survey of old and new results is available in [51].”
On sum sets of sets having small product set (2015, neutral): “On the one hand, a general upper bound for the number of such triples in Cartesian products ([13], Corollary 8.”
Additive properties of product sets in fields of prime order (2007, neutral): “Some facts related to the harmonic analyisis in Z p can be found in ([5], Chapter 4).”
Solution of the minimum modulus problem for covering systems (2013, background): “For completeness, we show the argument in Appendix B; see also [18].”
Nonlinear large deviations (2014, background): “An excellent survey of old and new results is available in Tao and Vu [32].”
The smallest singular value of a random rectangular matrix (2008, methodology): “To estimate the L´evy concentration function we apply the Ess´een Lemma, see e.g. [23], p. 290.”
Additive Combinatorics and Discrete Logarithm Based Range Protocols (2010, background): “Moreover, for an integer b and A ⊂ Z, b ∗A = {ba : a ∈ A}, this is also called the b-dilate of A [17].”
Small Ball Probability, Inverse Theorems, and Applications (2012, neutral): “In [21] (see also in [67]), Halász proved the following very general theorem.”
Inverse Littlewood-Offord problems and The Singularity of Random Symmetric Matrices (2011, background): “In [8] (see also in [25]), Halász proved very general theorems that imply the SárkőzySzemerédi theorem and many others.”
Arithmetic Progressions in Sets of Fractional Dimension (2007, methodology): “We rely on many of the ideas from [24], [12], and particularly [14], [30], such as the use of the trilinear form Λ in a Fourier representation and a decomposition of the measure μ into “random” and “periodic” parts.”