Ju n 20 01 New Approach to Ohno Relation for Multiple Zeta Values
نویسندگان
چکیده
The weight and the depth of ζ(k1, . . . , km) are k1 + · · ·+ km and m, respectively. Recently, MZVs have been studied extensively in number theory [Go, Z], knot theory [LM], mirror symmetry [H3] and perturbative quantum field theory [Kr]. Many relations of MZVs, for example Hoffman’s relation [H1], the duality formula [Z], the sum formula [Gr], Le-Murakami’s relation [LM] and the cyclic sum formula [HO], have been discovered. In particular, Ohno discovered a systematic relation which contain Hoffman’s relation, the duality formula and the sum formula. These relations are important to consider the structure of Z, which is an algebra over Q generated by all the MZVs.
منابع مشابه
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متن کاملar X iv : m at h / 04 02 15 2 v 1 [ m at h . Q A ] 1 0 Fe b 20 04 On relations for the q - multiple zeta values
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متن کاملar X iv : m at h / 00 10 14 0 v 1 [ m at h . Q A ] 1 3 O ct 2 00 0 RELATIONS OF MULTIPLE ZETA VALUES AND THEIR ALGEBRAIC EXPRESSION
We establish a new class of relations among the multiple zeta values ζ(k1, . . . , kl) = ∑ n1>···>nl≥1 1 n k1 1 · · ·n kl k , which we call the cyclic sum identities. These identities have an elementary proof, and imply the “sum theorem” for multiple zeta values. They also have a succinct statement in terms of “cyclic derivations” as introduced by Rota, Sagan and Stein. In addition, we discuss ...
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تاریخ انتشار 2001