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When I was reading Folland's A course in abstract harmonic analysis, I was told these materials have wonderful applications to number theory. However, I do not see really a lot of examples there.

Can someone give some references on the applications of harmonic analysis to number theory?

I am asking this question because I am trying to figure out what to do in my coming graduate years. I have learnt a lot analysis but I do not really like doing hard analysis all day, so maybe some application of analysis to other parts of mathematics suits me better.

Thanks so much!

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  • $\begingroup$ Fourier analysis on number fields is relevant to $L$-functions for instance. $\endgroup$ – anon Jul 25 '13 at 9:22
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    $\begingroup$ I have only skimmed over it, but "Fourier Analysis on Number Fields" by Ramakrishnan and Valenza looks worth checking out. $\endgroup$ – Nils Matthes Jul 25 '13 at 11:20
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Hugh L. Montgomery, Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis.

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  • $\begingroup$ Too bad I don't have access to this. But thanks anyway! $\endgroup$ – Hui Yu Jul 25 '13 at 13:54
  • $\begingroup$ If you have access to a library, maybe they can get it for you on interlibrary loan. $\endgroup$ – Gerry Myerson Jul 25 '13 at 23:38

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