We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara,Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with one generator.We apply these results to ...We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara,Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with one generator.We apply these results to show that the full sets of shuffle relations of polylogarithms and regularized MZVs are derived by a single series.We also take this approach to study the extended double shuffle relations of MZVs by comparing these shuffle relations with the quasi-shuffle relations of the regularized MZVs in our previous approach of MZVs by renormalization.展开更多
基金support from NSF grant DMS-0505643support from National Natural Science Foundation of China (Grant Nos.10631050,10911120391/A0109)
文摘We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara,Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with one generator.We apply these results to show that the full sets of shuffle relations of polylogarithms and regularized MZVs are derived by a single series.We also take this approach to study the extended double shuffle relations of MZVs by comparing these shuffle relations with the quasi-shuffle relations of the regularized MZVs in our previous approach of MZVs by renormalization.
