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 |
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