Details:
Title  Lyndon words, polylogarithmic functions and the Riemann $zeta$function  Author(s)  Hoang Ngoc Minh, Michel Petitot  Type  Technical Report, Misc  Abstract  In this work, we explain the functional relations between polylogarithmic functions encoding them by words over non commutative variables. Evaluating these relations at z = 1, we found again the relations between the Euler/Zagier sums, especially the decomposition formula. We then compute a Groebner basis of the algebra generated by the Euler/Zagier sums. This computation uses the Lyndon words, which are a transcendence basis of the shuffle algebra. 
Language  English  Year  2005  Edition  0  Translation 
No  Refereed 
No 
