-Series with Applications to Combinatorics, Number Theory, and Physics
-Series with Applications to Combinatorics, Number Theory, and Physics
复制标题
DOI：
10.1090/conm/291
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
B. Berndt;K. Ono
中科院分区：
文献类型：
--
作者：
B. Berndt;K. Ono
级数的研究可以说是开始于欧拉和他的五边形数定理。事实上，级数有时也被称为欧拉级数。贡献是由高斯，雅可比，柯西，但第一次尝试在一个系统的发展，特别是从研究的角度来看，系列的产品在summands，是由E。1847年的海涅。在19世纪后半叶和20世纪初，两位英国数学家罗杰斯（LJ Rogers）和杰克逊（FH杰克逊）做出了重要贡献。在1940年，GH哈代描述了我们现在所说的拉马努金著名的求和定理“一个有许多参数的显着公式。“这现在是这个问题的基本定理之一。尽管开始时很不起眼，但在过去的三十年里，级数的主题已经蓬勃发展，特别是在组合学，数论和物理学中的应用。2000年，伊利诺伊大学迎来了数论千禧年。这一年的事件之一是会议系列与应用组合数学，数论，和物理。这次活动聚集了来自世界各地的数学家演讲和讨论他们的研究。本卷介绍了会议上提出的论文中的十九篇.优秀的讲座，包括图表路径到未来和调查的众多应用系列组合，数论和物理。
The subject of-series can be said to begin with Euler and his pentagonal number theorem. In fact,-series are sometimes called Eulerian series. Contributions were made by Gauss, Jacobi, and Cauchy, but the first attempt at a systematic development, especially from the point of view of studying series with the products in the summands, was made by E. Heine in 1847. In the latter part of the nineteenth and in the early part of the twentieth centuries, two Englishmathematicians, LJ Rogers and FH Jackson, made fundamental contributions. In 1940, GH Hardy described what we now call Ramanujan's famoussummation theorem as``a remarkable formula with many parameters.''This is now one of the fundamental theorems of the subject. Despite humble beginnings, the subject of-series has flourished in the past three decades, particularly with its applications to combinatorics, number theory, and physics. During the year 2000, the University of Illinois embraced The Millennial Year in Number Theory. One of the events that year was the conference-Series with Applications to Combinatorics, Number Theory, and Physics. This event gathered mathematicians from the world over to lecture and discuss their research. This volume presents nineteen of thepapers presented at the conference. The excellent lectures that are included chart pathways into the future and survey the numerous applications of-series to combinatorics, number theory, and physics.