| 书目名称 | The Power of q |
| 副标题 | A Personal Journey |
| 编辑 | Michael D. Hirschhorn |
| 视频video | |
| 概述 | Aptly conveys the beauty and power of q-series.Accessible to advanced undergraduates, graduate students, and researchers.Historical notes enrich the readers understanding of the subject.First monograp |
| 丛书名称 | Developments in Mathematics |
| 图书封面 |  |
| 描述 | .This unique book explores the world of q, known technically as basic hypergeometric series, and represents the author’s personal and life-long study—inspired by Ramanujan—of aspects of this broad topic. While the level of mathematical sophistication is graduated, the book is designed to appeal to advanced undergraduates as well as researchers in the field. The principal aims are to demonstrate the power of the methods and the beauty of the results. The book contains novel proofs of many results in the theory of partitions and the theory of representations, as well as associated identities. Though not specifically designed as a textbook, parts of it may be presented in course work; it has many suitable exercises..After an introductory chapter, the power of q-series is demonstrated with proofs of Lagrange’s four-squares theorem and Gauss’s two-squares theorem. Attention then turns to partitions and Ramanujan’s partition congruences. Several proofs of these are given throughout the book. Many chapters are devoted to related and other associated topics. One highlight is a simple proof of an identity of Jacobi with application to string theory. On the way, we come across the Rogers–Ram |
| 出版日期 | Book 2017 |
| 关键词 | q-series; Ramanujan partition congruences; dissection Euler product; hypergeometric series; quintuple pr |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-57762-3 |
| isbn_softcover | 978-3-319-86241-5 |
| isbn_ebook | 978-3-319-57762-3Series ISSN 1389-2177 Series E-ISSN 2197-795X |
| issn_series | 1389-2177 |
| copyright | Springer International Publishing AG 2017 |
发表于 2025-3-21 18:45:35
