General systems of linear forms: equidistribution and true complexity (Q5965073)
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scientific article; zbMATH DE number 6548171
| Language | Label | Description | Also known as |
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| English | General systems of linear forms: equidistribution and true complexity |
scientific article; zbMATH DE number 6548171 |
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General systems of linear forms: equidistribution and true complexity (English)
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2 March 2016
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higher-order Fourier analysis
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additive combinatorics
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linear patterns
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nonclassical polynomials
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The paper is a continuation of the authors' previous paper [\textit{A. Bhattacharyya} et al., in: Proceedings of the 45th annual ACM symposium on theory of computing, STOC 2013. Palo Alto, CA, USA, June 1--4, 2013. New York, NY: ACM, 429--436 (2013; Zbl 1293.11016)]. The density of a linear system in subsets of Abelian groups is analysed by high-order Fourier analysis.NEWLINENEWLINEA complete characterization for a special type of distributions for arbitrary systems of linear forms is given.NEWLINENEWLINESome interesting applications are discussed, one of which -- an idea for a new theory of homogeneous non-classical polynomials.
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