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Euler's formulae for $\zeta(2n)$ and products of Cauchy variables

   
@article{ECP1244,
	author = {Paul Bourgade and Takahiko Fujita and Marc Yor},
	title = {Euler's formulae for $\zeta(2n)$ and products of Cauchy variables},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {12},
	year = {2007},
	keywords = {Cauchy variables, stable variables, planar Brownian motion, Euler numbers.},
	abstract = {We show how to recover Euler's formula for  $\zeta(2n)$, as well as $L_{\chi_4}(2n+1)$, for any integer $n$,  from the knowledge of the density of the product  $\mathbb{C}_1,\mathbb{C}_2\ldots,\mathbb{C}_k$, for any $k\geq 1$, where the $\mathbb{C}_i$'s are  independent standard Cauchy variables.},
	pages = {no. 9, 73-80},
	issn = {1083-589X},
	doi = {10.1214/ECP.v12-1244},    
        url = {http://ecp.ejpecp.org/article/view/1244}}