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


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.


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Paul Bourgade. Takahiko Fujita. Marc Yor. "Euler's formulae for $\zeta(2n)$ and products of Cauchy variables." Electron. Commun. Probab. 12 73 - 80, 2007.


Accepted: 7 April 2007; Published: 2007
First available in Project Euclid: 6 June 2016

zbMATH: 1129.60088
MathSciNet: MR2300217
Digital Object Identifier: 10.1214/ECP.v12-1244

Keywords: Cauchy variables , Euler numbers , Planar Brownian motion , stable variables

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