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Four variants of the Fourier-analytic transference principle

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>1/09/2017
<mark>Journal</mark>Online Journal of Analytic Combinatorics
Issue number12
Number of pages25
Publication StatusPublished
<mark>Original language</mark>English


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.