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

Paul Bourgade, Takahiko Fujita, Marc Yor

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)73-80
Number of pages8
JournalElectronic Communications in Probability
StatePublished - Jan 1 2007


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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