Higher-Order Fourier Analysis Of $${\mathbb{F}_{p}^n}$$ And The Complexity Of Systems Of Linear Forms

Bergelson V., Tao T., Ziegler T.: An inverse theorem for the uniformity seminorms associated with the action of $${\mathbb{F}_{p}^\infty}$$ . Geom. Funct. Anal. 19, 6 1539–1596 (2010)

Gowers W.T.: A new proof of Szemerédi’s theorem. Geom. Funct. Anal. 11(3), 465–588 (2001)

Gowers W.T.: Decompositions, approximate structure, transference, and the hahn-banach theorem. Bull. London Math. Soc. 42(4), 573–606 (2010)

Gowers W.T., Wolf J.: The true complexity of a system of linear equations. Proc. Lond. Math. Soc. (3). 100(1), 155–176 (2010)

Gowers W.T., Wolf J.: Linear forms and higher-degree uniformity for functions on $${\mathbb{F}_{p}^n}$$ . Geom. Funct. Anal. 21(1), 36–69 (2011)

B. Green, Montréal notes on quadratic Fourier analysis, in “Additive Combinatorics”, CRM Proc. Lecture Notes 43, Amer. Math. Soc., Providence, RI (2007), 69–102.

Green B., Tao T.: The distribution of polynomials over finite fields, with applications to the Gowers norms. Contrib. Discrete Math. 4(2), 1–36 (2009)

B. Green, T. Tao, An arithmetic regularity lemma, associated counting lemma, and applications, in “In Honour of the 70th Birthday of Endre Szemeredi”, to appear.

Green B., Tao T.: Linear equations in primes. Ann. of Math. (2) 171(3), 1753–1850 (2010)

H. Hatami, S. Lovett, Correlation testing for affine invariant properties on Fnp in the high error regime, in “STOC ’11: Proceedings of the 43th Annual ACM Symposium on Theory of Computing”, ACM, New York, NY, USA, to appear.

T. Kaufman, S. Lovett, Worst case to average case reductions for polynomials, in “FOCS ’08: Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science”, Washington, DC, USA, IEEE Computer Society (2008), 166– 175.

Roth K.F.: On certain sets of integers. J. London Math. Soc. 28, 104–109 (1953)

E. Szemerédi, On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27 (1975), 199–245 (Collection of articles in memory of Juriĭ Vladimirovič Linnik.)

T. Tao, Some notes on “non-classical” polynomials in finite characteristic, online blog, http://terrytao.wordpress.com/2008/11/13/some-notes-on-nonclassical-polynomials-in-finite-characteristic

T. Tao, T. Ziegler, The inverse conjecture for the gowers norm over finite fields in low characteristic, preprint; $${\tt arXiv:1101.1469}$$

Tao T., Ziegler T.: The inverse conjecture for the Gowers norm over finite fields via the correspondence principle. Anal. PDE 3(1), 1–20 (2010)