Integral Structures of Multiple Polylogarithms at Roots of Unity
نویسندگان
چکیده
In this paper, for any positive integer N we shall study the special values of multiple polylogarithms at Nth roots of unity, called multiple polylogarithmic values (MPVs) of level N . By standard conjectures linear relations exist only between MPVs of the same weight. LetMPVZ(w,N) be the Z-module spanned by MPVs of weight w and level N . Our main interest is to investigate for what w and N there exists a basis consisting of MPVs in MPVZ(w,N). In the scope of our investigation this problem always seems to have affirmative answers except for multiple zeta values (level one MPVs) of weight 6 and 7, provided that the conjectural dimensions of MPVQ(w,N) are correct.
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تاریخ انتشار 2009