All New Theories of Multiple Zeta Values [Eie] 9789865647483

This is the trilogy of author’s monograps in number theory, as a continuation of “Topics in Number Theory” published in 2009 and “The Theory of Multiple Zeta Values with Applications in Combinatorics” published in 2013. All these books were adopted from the lecture notes of the graduate course “Theory of Modular Forms of Several Variables” taught at Department of Mathematics, National Chung Cheng University since 1991. The Euler decomposition, the sum formula and the restricted sum formula were extended to cover all kind of duality theorems. Especially, multiple zeta values with parameters were first introduced to solve complicated problems concerning the sum formula.

頁數：314
版次：第1版
年份：2016年
規格：精裝/單色
ISBN：9789865647483

I Decomposition Theorems From Shuffle Products of Multiple Zeta Values
1 The New World of Multiple Zeta Values
2 Integral Representations fo Multiple Zeta Values
3 Decomposition Theorems of Riemann Zeta Values
4 Shuffle Product of Multiple Zeta Values of Height One
5 Applicatinos of the Decomposition Theorems
II Multiple Zeta Values with Parameters
6 Weighted Sum Formulas and Bernoulli Identities
7 Multiple Zeta Values with Parameters
8 Sum Formulas and Duality Theorems
9 All About the Restricted Sums
10 Back to the Decomposition Theorem
11 A Brief Survey of Multiple Zeta Values
III Appendix
A Evaluations of the Multiple Zeta Value