Polylogarithms and multiple zeta values from free Rota-Baxter algebras  

作　　者：GUO Li1,2 & ZHANG Bin3,1Center of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China 2Department of Mathematics and Computer Science,Rutgers University,Newark,NJ 07102,USA 3Yangtze Center of Mathematics,Sichuan University,Chengdu 610064,China 

出　　处：《Science China Mathematics》2010年第9期2239-2258,共20页中国科学：数学（英文版）

基　　金：support from NSF grant DMS-0505643;support from National Natural Science Foundation of China (Grant Nos.10631050,10911120391/A0109)

摘　　要：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.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.

关 键 词：multiple zeta values POLYLOGARITHMS Rota-Baxter ALGEBRAS 

分 类 号：O153[理学—数学]