Examples of proofs that use the (Hardy-Littlewood) Circle Method

Asked Mar 23 '20 at 14:22

Active Mar 23 '20 at 14:44

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I will be doing my bachelor thesis on the Hardy-Littlewood circle method, where in part I want to assess the value of this method. To do this, I want to look at some proofs that make use of this method. So,

Can you give any examples of proofs that use the circle method?

I want to see how the method contributed to the proof, including how the theorem was proved beforehand (if at all).

I will be using the following resource a lot,

https://web.williams.edu/Mathematics/sjmiller/public_html/BrownClasses/1/circlemethod.pdf

It contains a lot of very useful things, but I was hoping to find some other, perhaps more obscure, proofs to investigate.

edited Mar 23 '20 at 14:44

asked Mar 23 '20 at 14:22

Sandstar

Can you give examples for circle method proofs you found by googling? What about weak Goldbach? – Dietrich Burde Mar 23 '20 at 14:35
Updated to reflect a missing nuance – Sandstar Mar 23 '20 at 14:45
1

Well, Weak Goldbach is really more interesting than some "more obscure" topic. Also have a look here for example, how to use circle method for it, or this post. This should make a nice bachelor thesis. – Dietrich Burde Mar 23 '20 at 14:48

Examples of proofs that use the (Hardy-Littlewood) Circle Method

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