A new formula for ζ(2n + 1) (and how not to prove that ζ(5) is irrational)

Abstract : Using a new polylogarithmic identity, we express the values of ζ at odd integers 2n + 1 as integrals over unit n−dimensional hypercubes of simple functions involving products of logarithms. We then make several conjectures, based on numerical evidence, on the behaviour of those functions as some of their variables are raised to a power. Finally, we discuss how one attempt to adapt Beukers' integral-based proof of the irrationality of ζ(2) and ζ(3) to the case of ζ(5) fails.
Document type :
Preprints, Working Papers, ...
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01352764
Contributor : Thomas Sauvaget <>
Submitted on : Friday, October 28, 2016 - 12:36:17 PM
Last modification on : Monday, April 9, 2018 - 12:20:04 PM

Files

polylog_zetaodd_v2_Thomas_Sauv...
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution - NoDerivatives 4.0 International License

Identifiers

  • HAL Id : hal-01352764, version 2
  • ARXIV : 1608.03174

Citation

Thomas Sauvaget. A new formula for ζ(2n + 1) (and how not to prove that ζ(5) is irrational). 2016. ⟨hal-01352764v2⟩

Share

Metrics

Record views

77

Files downloads

26