The Theory of Partitions
The Theory of Partitions
复制标题
DOI：
10.1007/978-0-8176-4838-1_7
复制
发表时间：
1984
期刊：
影响因子：
--
通讯作者：
E. Grosswald
中科院分区：
文献类型：
--
作者：
E. Grosswald
自 18 世纪以来，分区理论引起了一些最优秀的学者的兴趣。虽然它看起来几乎没有实际应用，但从某种意义上来说，它的难度恰到好处。这些问题绝非微不足道，但同时它们也没有困难到阻碍任何解决方案的尝试。此外，通过欧拉（1707-1783）引入生成函数，高度发达的函数论装置可用于划分的研究。对本研究有很大帮助的另一个事实是，分分理论中出现的生成函数以及与之密切相关的函数属于两类重要的函数，即 theta 函数和模函数，自雅可比时代（1804-1851）以来，这两类函数都受到了广泛的关注并得到了最彻底的研究。
Since the 18th century the theory of partitions has interested some of the best minds. While it seems to have little or no practical application, it has, in a certain sense, just the right degree of difficulty. The problems are far from trivial, but at the same time they are not so hard as to discourage any attempt at a solution. Besides, through the introduction by Euler (1707–1783) of generating functions, the highly developed apparatus of the theory of functions became available for the study of partitions. A further circumstance of great help in this study is the fact that the generating functions which occur in the theory of partitions and functions closely related to them belong to two important classes of functions, namely the theta functions and the modular functions, both of which have received much attention and have been most thoroughly investigated since the time of Jacobi (1804–1851).