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TitleLyndon words, polylogarithmic functions and the Riemann $zeta$-function
Author(s) Hoang Ngoc Minh, Michel Petitot
TypeTechnical Report, Misc
AbstractIn 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.
Translation No
Refereed No