Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

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• 作者：Douglas Bowman and David M. Bradley
• 关键词：multiple zeta values ; MZV ; multiple polylogarithms ; Euler sums ; hypergeometric functions
• 刊名：Compositio Mathematica
• 出版年：2003
• 出版时间：2003
• 年：2003
• 卷：139
• 期：1
• 页码：85-100
• 全文大小：149 KB

文摘

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst–Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.