Study on special functions in q-analysis

点击翻译按钮获取中文摘要

Through the years from 2000 to 2003, I have been studying "Multiple Zeta Values" (MZVs, for short). I have written two articles on this theme: "New Approach to Ohno Relation for Multiple Zeta Values" (by Jun-ichi Okuda and Kimio Ueno, arXive:math.NT/0106148), "Relations for Multiple Zeta Values and Mellin Transforms of Multiple Polylogarithms" (by Jun-ichi Okuda and Kimio Ueno, arXive:math.NT/0301277). The latter article is an enlarged version of the former, and I submitted the latter to Publications of RIMS, Kyoto University.In recent progress of study, I revealed that relations satisfied by MZVs can be regarded, via inverse Mellin transform - Mellin transform, as the monodromy problem of the multiple polylogarithms (MPLs, for short). In the article submitted, I showed that the Ohno relations for MZVs are, in a sense, equivalent to the Landen connection formulas for MPLs.To the international conference "Zeta Functions, Topology and Quantum Physics" held at Kinki University, from March 3rd to March 6th (2003), Jun-ichi Okuda, who is a graduate student at Department of Mathematics, Waseda University, and the collaborators of this study, was invited and gave on hour lecture on this theme.