What are some good resources to learn arithmetic combinatorics? I have been very intrigued by the theory of arithmetic combinatorics after the result regarding primes in arithmetic progressions proven by Tao and Green.
PAPERS ARE OK. I notice that most people usually skip out on papers, but papers are what got me into the theory. I have found a book, (additive combinatorics-Tao), which so far seems quite nice. But for instance, are there any notes, or "paper-notes" or EVEN lectures based around, or even on this topic? Even some other books talking about this theory, or things related to that?
(I have watched the Ben Green lectures on higher-order Fourier analysis, and I am aware of Tao's notes on this subject).
 A: By no means am I an expert on this, so I don't know how good these resources are. However, these are other resources you might find helpful:

*

*https://www.amazon.com/Additive-Combinatorics-Proceedings-Lecture-Notes/dp/0821843516

*https://math.stanford.edu/~ksound/Notes.pdf

*http://people.maths.ox.ac.uk/greenbj/notes.html
Additive Combinatorics is also known as Discrete Harmonic Analysis in some circles (no pun intended). There is a book on Discrete Harmonic Analysis here:

*

*https://www.maa.org/press/maa-reviews/discrete-harmonic-analysis
If you are interested in a Theoretical Computer Science perspective, there are a couple good starting points:

*

*Daniel Stefankovic's Master's Thesis surveying applications of the Fourier transform in Combinatorics and TCS. (https://people.cs.uchicago.edu/~laci/students/stefankovic-masters.pdf)

*Ryan O'Donnell's book on Analysis of Boolean Functions (https://www.amazon.com/Analysis-Boolean-Functions-Ryan-ODonnell/dp/1107038324#reader_1107038324).

*Ryan O'Donnell's course webpage in this same area (https://www.cs.cmu.edu/~odonnell/boolean-analysis/).

I hope this is helpful!
