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.
Citation
Paul Bourgade. Takahiko Fujita. Marc Yor. "Euler's formulae for $\zeta(2n)$ and products of Cauchy variables." Electron. Commun. Probab. 12 73 - 80, 2007. https://doi.org/10.1214/ECP.v12-1244
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