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How can I use the Poisson summation formula to prove that $\zeta(2)= \pi^{2} \,/\, 6$ ? Using the Fourier transform of $\exp\left(-\left\lvert ax \right\rvert \right)$ gives a direct expression for the series $\frac{1}{ a^2+n^2 }$ but il can't find a way to prove it for the $1\,/\,n^2$ series.

Vlad
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unkindq
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    Before asking any question on how to prove $\zeta(2) = \pi^2/6$, be sure to check http://secamlocal.ex.ac.uk/people/staff/rjchapma/etc/zeta2.pdf where Robin Chapman collected many proofs. – GEdgar Aug 11 '15 at 01:22
  • Here is a long list of ways to prove it. Maybe it's in there (but I could not find it). – Winther Aug 11 '15 at 02:18
  • Thanks for the link. I just checked it and could not find it neither – unkindq Aug 11 '15 at 02:25
  • http://www.libragold.com/blog/2014/12/poisson-summation-formula-and-basel-problem/ – Adam Saltz Aug 11 '15 at 03:55

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