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研究生： 黃楷雯
Huang, Kai-Wen
論文名稱： 正特徵的多重zeta 星值
On multiple zeta star values in positive characteristic
指導教授： 張介玉
Chang, Chieh-Yu
口試委員: 于靖
王姿月
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2017
畢業學年度： 105
語文別： 英文
論文頁數： 21
中文關鍵詞： 多重zeta星值 、函數體
外文關鍵詞： multiple zeta star values, multiple polylogarithms
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    • 在這篇文章中，我們先定義在函數體F_q(\theta) 上的有限多重zeta 星值以及有限Carlitz 多重星多對數函數。接著我們證明了每一個正特徵的多重zeta 星值都可以寫成 Carlitz 多重星多對數函數在一些整數點上的F_q(\theta)-線性組合。

    In this paper, we define finite multiple zeta star values over the rational function field F_q(\theta) and also finite Carlitz multiple star polylogarithms. We show that every (finite) multiple zeta star value in positive characteristic is a F_q(\theta)-linear combination of (finite) Carlitz multiple star polylogarithms at some integral points.

    1 Introduction 1 1.1 Multiple zeta values 1 1.2 Finite multiple zeta values 2 2 A relation between MZSVs and CMSPLs 4 2.1 Definitions of MZSVs and CMSPLs 4 2.2 A formula between MZSVs and CMSPLs 6 3 A relation between FMZSVs and FCMSPLs 10 3.1 Definitions of FMZSVs and FCMSPLs 10 3.2 A formula between FMZSVs and FCMSPLs 12 4 Some remarks 15 4.1 Some properties for CMSPLs 15 4.2 Products of power sums 18 4.3 Generating functions 19 5 References 21

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