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Besides the Prime Number Theorem,

what other proofs are there that are proved via Complex Analysis?

[Mainly want to learn how these proof techniques work.]

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Please see the "how to ask" page. Mathoverflow is mainly designed for specific and focused research level questions, even though sometimes questions about intuition, the big picture, or a list of examples are also appropriate (provided the asker has specified why they are interested and what work they have done already). The question about applications of complex analysis is too broad, and can not be fully answered here... – Gjergji Zaimi Aug 27 2011 at 15:09
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 ...I suggest you try to improve your question, and don't forget that specifying your motivation for asking the question as well as providing the background you have (in complex analysis in this case) are also very important. – Gjergji Zaimi Aug 27 2011 at 15:09
Do you mean theorems whose statements do not involve complex numbers, but whose proofs do? – Steven Gubkin Aug 27 2011 at 15:09
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 For complex analysis in number theory you could have a look at the following question mathoverflow.net/questions/43464/… From your question, it is not clear to me whether you wish to restrict to number theory applications. I agree with Gjergji that without some restriction the question seems too broad. – quid Aug 27 2011 at 15:21

closed as off topic by Andres Caicedo, Gjergji Zaimi, Zev Chonoles, Steven Gubkin, Mark Sapir Aug 27 2011 at 15:18

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