拟Theta函数的模变换性质

发布时间：2018-04-15 17:58

本文选题：拟v-函数 + 模形式　；参考：《中国科学技术大学》2017年硕士论文

【摘要】：拟v-函数作为经典模形式的一类推广,自Ramanujan于1920年提出其概念以来,受到了广泛的关注与研究,并在现代数学中扮演越来越重要的角色。本论文是S.Zwegers关于拟v-函数理论的工作的综述,重点总结推导拟v-函数模变换性质的方法,以及讨论拟v-函数同经典模形式的关系。模变换性质在拟v-函数理论中具有基本而重要的地位。第一章在介绍基本概念的基础上,通过计算一个三阶拟v-函数的例子,体现拟v-函数的模变换性质的特点,为之后的理论提供背景。第二章引入需要用到的若干理论工具,特别是非正定v-函数的概念与性质。第三章具体推导七阶与五阶v-函数的模变换性质,这是通过建立拟v-函数与非正定v-函数之间的联系来实现的。
[Abstract]:Quasi-v-function, as a kind of generalization of classical modular form, has been paid more and more attention and research since Ramanujan put forward its concept in 1920, and plays an increasingly important role in modern mathematics.This paper is a review of S.Zwegers 's work on quasi v-function theory, focusing on the methods of deducing the properties of quasi-v-function modulus transformation, and discussing the relation between quasi v-function and classical modular form.The property of modular transformation plays a fundamental and important role in the theory of quasi-v-function.In the first chapter, based on the introduction of the basic concepts, an example of a third-order quasi-v-function is calculated to show the properties of the modular transformation of the quasi-v-function, which provides the background for the later theory.In the second chapter, some theoretical tools are introduced, especially the concept and properties of nonpositive definite v-functions.In chapter 3, the modular transformation properties of the seventh and fifth order v-functions are derived, which is realized by establishing the relationship between quasi-v-functions and non-positive definite v-functions.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O174.6

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