Cargando…
The theory of multiple zeta values with applications in combinatorics /
This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, and numerous interesting identities are produced that are ready to be used. Thi...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Hackensack] New Jersey :
World Scientific,
©2013.
|
| Colección: | Monographs in number theory ;
v. 7. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- I. Basic theory of multiple zeta values. 0. The time before multiple zeta values. 0.1. The evaluation of Euler double sums. 0.2. Vandermonde convolution. 0.3. Zeta functions associated with multiple zeta values. 0.4. Messages from modular forms
- 1. Introduction to the theory of multiple zeta values. 1.1. Introduction and notations. 1.2. Drinfeld integral representations of multiple zeta values. 1.3. Double weighted sum formulas. 1.4. The expectations of binomial distributions. 1.5. Exercises
- 2. The sum formula. 2.1. Through the integral representations. 2.2. Another proof of the sum formula. 2.3. Evaluation of multiple zeta values of height one. 2.4. Exercises
- II. Shuffle relations among multiple zeta values. 3. Some shuffle relations. 3.1. Shuffle relations of multiple zeta values. 3.2. An application of double weighted sums. 3.3. Shuffle relations of two sums of multiple zeta values. 3.4. A vector version of the restricted sum formula. 3.5. Exercises
- 4. Euler decomposition theorem. 4.1. A shuffle relation with two parameters. 4.2. Integrals with three factors. 4.3. Generalizations of Euler decomposition theorem. 4.4. Applications of the decomposition theorem. 4.5. Applications of another decomposition theorem. 4.6. Exercises
- 5. Multiple zeta values of height two. 5.1. Sums of multiple zeta values of height two. 5.2. Weighted sums of multiple zeta values of height two. 5.3. The shuffle product formula of a sum and others. 5.4. Exercises
- III. Applications of shuffle relations in combinatorics. 6. Generalizations of Pascal identity. 6.1. Applications of shuffle products in combinatorics. 6.2. Hypergeometric distribution. 6.3. The generating function of three variables. 6.4. Exercises
- 7. Combinatorial identities of convolution type. 7.1. Some particular combinatorial identities. 7.2. A generating function for products. 7.3. A combinatorial identity of convolution type. 7.4. Another generating function of three variables. 7.5. Exercises
- 8. Vector versions of some combinatorial identities. 8.1. The shuffle product of two sums. 8.2. More combinatorial identities of convolution type. 8.3. Vector versions of Pascal identity. 8.4. Problems on combinatorial identity.