Fourier transforms and solving linear equations
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If you have a question about this talk, please contact Anton Evseev.
Additive combinatorics is a subject in which one often uses techniques
from unexpected areas of mathematics in order to solve simpletostate
problems. An example of this is the use of Fourier analysis in
dealing with solutions to linear equations in sets of integers. The aim of
this talk is to describe some of these basic techniques, including some of
the Fourier analysis and some of the oftused averaging methods. We will
focus in particular on how such techniques may be used to prove Roth’s
theorem on arithmetic progressions. If time permits, we will also
describe a cute link with evaluating some Dirichlet series.
This talk is part of the Junior Algebra and Number Theory seminar series.
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