Four variants of the Fourier-analytic transference principle

Prendiville, Sean (2017) Four variants of the Fourier-analytic transference principle. Online Journal of Analytic Combinatorics (12). ISSN 1931-3365

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Abstract

We survey four instances of the Fourier analytic ‘transference principle’ or ‘dense model lemma’, which allows one to approximate an unbounded function on the integers by a bounded function with similar Fourier transform. Such a result forms a component of a general method pioneered by Green to count solutions to a single linear equation in a sparse subset of integers.