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Showing 1 to 2 of 2 for “"Higher-order Fourier Analysis"”.
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Higher-order Fourier analysis with applications to additive combinatorics and theoretical computer science
Fourier analysis has been used for over one hundred years as a tool to study certain additive patterns. For example, Vinogradov used Fourier-analytic techniques (known in this context as the Hardy-Littlewood circle method) to show that every sufficiently-large odd integer can be written as the sum …
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Arithmetic regularity lemmas and applications
… setting. The rest of the thesis concerns higher-order arithmetic regularity, in particular undertaking a study of local higher-order uniformity in Chapter 3. Two approaches to defining local uniformity on polynomial factors are proposed and subsequently applied to generalise two theorems …