Resolution of some open problems concerning multiple zeta evaluations of arbitrary depth

被引：25

作者：

Bowman, D ^{[1
]}

Bradley, DM

机构：

[1] No Illinois Univ, Dept Math, Dept Math Sci, De Kalb, IL 60115 USA

[2] Univ Maine, Dept Math & Stat, Orono, ME 04469 USA

来源：

COMPOSITIO MATHEMATICA | 2003年 / 139卷 / 01期

基金：

美国国家科学基金会;

关键词：

multiple zeta values; MZV; multiple polylogarithms; Euler sums; hypergeometric functions;

D O I：

10.1023/B:COMP.0000005036.52387.da

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：85 / 100

页数：16

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