Linear independence of hyperlogarithms

Matthieu Deneufchatel

Description

Linear independence of hyperlogarithms Matthieu Deneufchatel Laboratoire d'Informatique de Paris Nord, Universite Paris 13 Joint work with Gerard H. E. Duchamp, H. N. Minh, A. I. Solomon EJC GDR-IM, 29 Mars 2011

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• free monoid

Sujets

• Van (Dutch)
• Free monoid

Informations

• Publié par: profil-urra-2012
• Publié le: 01 mars 2011
• Nombre de lectures: 18
• Langue: English

Extrait

Linear independence of hyperlogarithms

MatthieuDeneufchaˆtel

Laboratoire d’Informatique de Paris Nord, Universit´eParis13

JointworkwithGe´rardH.E.Duchamp,H.N.Minh,A.I.Solomon

EJC GDR-IM, 29 Mars 2011

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4

Integrator and differential equation

Theorems and application to hyperlogarithms

8

Introduction

Outline

2

1

3

Algebra of the free monoid over a differential ring

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Definition ds n L(a 0     a n |zz) = Z z 0 z Z z 0 s n    Z z 0 s 1 s 0 d − s 0 a 0 s n −a n 0    

Of ordern; Introduced in 1928 by Lappo-Danilevski; Ifz 0 6=a i ∀i, the integrals converge. Drinfel’d equation :dS=  x z 0 1 + x − 1 z  S.

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