General systems of linear forms: Equidistribution and true complexity

Advances in Mathematics, pp. 446-477, 2016.

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Keywords:
Higher-order Fourier analysisAdditive combinatoricsLinear patternsNonclassical polynomials

Abstract:

Higher-order Fourier analysis is a powerful tool that can be used to analyze the densities of linear systems (such as arithmetic progressions) in subsets of Abelian groups. We are interested in the group Fpn, for fixed p and large n, where it is known that analyzing these averages reduces to understanding the joint distribution of a famil...More

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