臺灣博碩士論文加值系統

在本篇論文的第一節裡,我們一開始先介紹古典尤拉和與多重 zeta 值。
第二節我們使用多重 zeta 值的積分表現式來處理 Drinfeld 對偶性定理。
第三節,利用多重 zeta 值的和可表成重積分形式以及透過連續兩次的變數變換,我們證明出多重 zeta 值的求和公式及受限制的求和公式。
在最後一節裡,我們處理含兩個變數的三重 zeta 值的等式且透過對特定的變數微分,得到當權是偶數時三重 zeta 值的計算公式。
在此,我們給出權等於 8 和 10 的精確三重 zeta 值。

In section 1, we begin with the introduction of classical Euler sums and multiple zeta values.
In section 2, the integral representation of multiple zeta values is used to deal with the Drinfeld duality theorem.
In section 3, applying a sum of multiple zeta values as a double integral and through two consecutive changes of variables, we demonstrate the sum formula and the restricted sum formula.
In the final section, we produce identities involving triple zeta values with two variables and perform differentiation with respect to the specified variable. This leads to the evaluation of triple Euler sums (the multiple zeta values for r=3) when the weight is even. Here we give the explicit evaluation of triple Euler sums of weight 8 and 10.

Abstract
1. Classical Euler sums and multiple zeta values
2. Drinfeld integral and duality
3. The sum formula and restricted sum formula
4. The evaluation of triple Euler sums for w=8,10
Reference

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