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The usual proofs in number theory books seem rather annoying if the goal is to actually be able to remember the proof in the future. At the same time these books typically assume that the reader's background is pretty light on complex analysis. In other words, are there any "easily memorizable" proofs assuming the reader has, say, taken the first year graduate level complex analysis class (i.e. knows all of Ahlfors)?

Supposedly there are also some proofs using class field theory. I'm also curious how they would work.

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Extensively discussed on MO: mathoverflow.net/questions/25794/… –  Qiaochu Yuan Nov 6 '11 at 23:17
    
Too bad we can't close-as-an-exact-duplicate-of-a-question-on-MathOverflow. –  Gerry Myerson Nov 7 '11 at 0:59
    
That didn't show up on google either, since $L(1,\chi)$ is hard to search for... Thanks. –  pki Nov 7 '11 at 2:21

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