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On the gowers norms of certain functions

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Abstract

We consider functions f(x, y) whose smallness condition for the rectangular norm implies the smallness of the rectangular norm for f(x, x + y). We also study families of functions with a similar property for the higher Gowers norms. The method of proof is based on a transfer principle for sums between special systems of linear equations.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    I. D. Shkredov

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  1. I. D. Shkredov
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Correspondence to I. D. Shkredov.

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Original Russian Text © I. D. Shkredov, 2012, published in Matematicheskie Zametki, 2012, Vol. 92, No. 4, pp. 609-2627.

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Shkredov, I.D. On the gowers norms of certain functions. Math Notes 92, 554–569 (2012). https://doi.org/10.1134/S0001434612090271

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