臺灣博碩士論文加值系統

古典的尤拉和當權數為奇數時可以用一些正值黎曼 zeta 函數值來計算。
本文,我們討論六個新的尤拉和家族的計算,即 K,L,M,C,T 和 D 家族,
和當權數為奇數時古典尤拉和帶偶 Dirichlet 特徵的計算。
我們證明以上都可用一些正值 Hurwitz zeta 函數來計算並且給出
一些計算值當權數很小時。

The classical Euler sums can be evaluated in terms of values at
positive integers of the Riemann zeta function when the weight is
odd. In this thesis, we discuss the evaluations of six families of
new Euler sums, namely K,L,M,C,T and D families, and the
classical Euler sums with an even Dirichlet character when the
weight is odd. We prove that they can be evaluated in terms of
values at positive integers of the Hurwitz zeta function and we
give some exact evaluations of them when the weight is small.

1. Classical Euler Sums
2. Building Blocks of Euler Sums
3. Another Triple Families: C,T,D
4. General Formulae
5. Euler Sums with Dirichlet Characters

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