### Abstract

We show how to recover Euler's formula for ζ(2n), as well as L _{χ4}(2n + 1), for any integer n, from the knowledge of the density of the product ℂ_{1}, ℂ_{2} . . . , ℂ_{k}, for any k ≥ 1, where the ℂ_{i}'s are independent standard Cauchy variables.

Original language | English (US) |
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Pages (from-to) | 81-88 |

Number of pages | 8 |

Journal | Electronic Communications in Probability |

Volume | 12 |

State | Published - Apr 7 2007 |

### Keywords

- Cauchy variables
- Euler numbers
- Planar Brownian motion
- Stable variables

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Bourgade, P., Fujita, T., & Yor, M. (2007). Euler's formulae for ζ(2n) and products of Cauchy variables.

*Electronic Communications in Probability*,*12*, 81-88.