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Analytic proof of quadratic reciprocity
Is there any proof of quadratic reciprocity that is more analytic than those described on Wikipedia (http://en.wikipedia.org/wiki/Proofs_of_quadratic_reciprocity)?

Yes, see http://mathoverflow.net/questions/1420/whats-the-best-proof-of-quadratic-reciprocity.

For a Fourier-analytic proof of quadratic reciprocity, see section $3$ of http://www.math.upenn.edu/~shanshand/research/08srthesis.pdf. 
