### 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) |
---|---|

Pages (from-to) | 73-80 |

Number of pages | 8 |

Journal | Electronic Communications in Probability |

Volume | 12 |

DOIs | |

State | Published - Jan 1 2007 |

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

## Fingerprint Dive into the research topics of 'Euler’s formulae for ζ(2n) and products of cauchy variables'. Together they form a unique fingerprint.

## 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*, 73-80. https://doi.org/10.1214/ECP.v12-1244