Équations fonctionnelles du dilogarithme

Abstract : This paper proves a " new " family of functional equations (Eqn) for Rogers dilogarithm. These equations rely on the combinatorics of dihedral coordinates on moduli spaces of curves of genus 0, M 0,n. For n = 4 we find back the duality relation while n = 5 gives back the 5 terms relation. It is then proved that the whole family reduces to the 5 terms relation. In the author's knownledge, it is the first time that an infinite family of functional equations for the dilogarithm with an increasing number of variables (n − 3 for (Eqn)) is reduced to the 5 terms relation.
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https://hal.archives-ouvertes.fr/hal-01196338
Contributor : Ismaël Soudères <>
Submitted on : Thursday, September 14, 2017 - 3:59:01 PM
Last modification on : Friday, September 15, 2017 - 1:02:10 AM
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  • HAL Id : hal-01196338, version 2
  • ARXIV : 1509.02869

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Ismaël Soudères. Équations fonctionnelles du dilogarithme. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2018. ⟨hal-01196338v2⟩

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