### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Electronic Communications in Probability*,

*12*, 73-80. https://doi.org/10.1214/ECP.v12-1244

**Euler’s formulae for ζ(2n) and products of cauchy variables.** / Bourgade, Paul; Fujita, Takahiko; Yor, Marc.

Research output: Contribution to journal › Article

*Electronic Communications in Probability*, vol. 12, pp. 73-80. https://doi.org/10.1214/ECP.v12-1244

}

TY - JOUR

T1 - Euler’s formulae for ζ(2n) and products of cauchy variables

AU - Bourgade, Paul

AU - Fujita, Takahiko

AU - Yor, Marc

PY - 2007/1/1

Y1 - 2007/1/1

N2 - We show how to recover Euler’s formula for ζ(2n), as well as Lχ4 (2n + 1), for any integer n, from the knowledge of the density of the product ℂ1,ℂ2., ℂk, for any k ≥ 1, where the ℂi’s are independent standard Cauchy variables.

AB - We show how to recover Euler’s formula for ζ(2n), as well as Lχ4 (2n + 1), for any integer n, from the knowledge of the density of the product ℂ1,ℂ2., ℂk, for any k ≥ 1, where the ℂi’s are independent standard Cauchy variables.

KW - Cauchy variables

KW - Euler numbers

KW - Planar Brownian motion

KW - Stable variables

UR - http://www.scopus.com/inward/record.url?scp=77955137928&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955137928&partnerID=8YFLogxK

U2 - 10.1214/ECP.v12-1244

DO - 10.1214/ECP.v12-1244

M3 - Article

AN - SCOPUS:77955137928

VL - 12

SP - 73

EP - 80

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

ER -