Problems in the Theory of Partitions and Q- Series

9400191阿拉迪该奖项资助克里希纳斯瓦米·阿拉迪教授在划分理论方面的研究。阿拉迪教授将尝试应用他与巴兹尔·戈登教授共同开发的一种新技术来解决五个问题。他将学习一个分拆定理MF Gollnitz，这是Capparelli最近的一个结果，q-Gauss恒等式和五重乘积恒等式。这项工作属于解析数论的一般领域，特别是分拆理论。在其最基本的层面上，划分理论研究的问题是，一个数字可以用多少种不同的方式写成较小数字的和？当这个问题的答案被编码成数学函数时，这个问题就成为解析数论的一部分。这使得数学家可以应用微积分的分析技术。使用连续方法研究离散物体的想法已经有两百年的历史了，但随着现代解析数学家的工作，该领域获得了新的新生，并导致了对整数划分的更深层次的理解。

9400191 Alladi This award funds the research of Professor Krishnaswami Alladi in partition theory. Prof. Alladi will try to apply a new technique that he developed in joint work with Prof. Basil Gordon to five problems. He will study a partition theorem mf Gollnitz, a recent result of Capparelli, the q-Gauss identities, and the quintuple product identity. This work is in the general field of analytic number theory and in particular partition theory. At its most basic level partition theory studies the question, how many different ways can one number be written as the sum of smaller numbers? This question becomes a part of analytic number theory when answers to this question are encoded into mathematical functions. This allows mathematicians to apply the analysis techniques of calculus. The idea of using continuous methods to investigate discrete objects is two centuries old, but with the work of the modern analytic number theorists, the field has had a new rebirth and led to a deeper understanding of partitions of the whole numbers.