US collaboration with Argentina, Chile, and Uruguay: Modular Forms in the Southern Cone

这项CNIC建议旨在支持巴克内尔大学的Nathan Ryan博士及其合作者、阿根廷布宜诺斯艾利斯大学的Ariel Pacetti博士、乌拉圭共和国大学的Gonzalo Tornaria博士和智利圣地亚哥大学的Yves Martin博士之间关于更高阶模形式的理论和计算研究的研究。模形式是数论中的一个重要课题。自从20世纪90年代Andrew Wiles证明了Fermat-S最后定理之后，许多基础性和计算性的工作使人们对一阶椭圆曲线的模形式和它们的L函数之间的关系有了相当完整的理解。PI和他的合作者希望将这种理解扩展到更高级别的模块形式。每个合作者都为项目带来了不同的专业知识，因此他们将能够处理许多不同的方法和主题。他们还将试图通过北美和南美洲研究人员之间的接触，以及让来自美国历史上代表性不足的群体的三名研究生与乌拉圭的同行互动，同时参与与排名大于一的模块形式有关的计算和理论研究项目，来传播和推动对模块形式的研究。

This CNIC proposal aims to support research between Dr. Nathan Ryan of Bucknell University and his collaborators, Dr. Ariel Pacetti of the Universidad de Buenos Aires, Argentina, Dr. Gonzalo Tornaria of the Universidad de la Republica in Uruguay, and Dr. Yves Martin of the Universidad de Chile, in Santiago, Chile, on the theoretical and computational study of modular forms of higher rank. Modular forms are an important subject within number theory. After Andrew Wiles proved Fermat?s Last Theorem in the nineties, much work of foundational and computational nature has led to a fairly complete understanding of the relationships between modular forms of rank one, elliptic curves, and their L-functions. The PI and his collaborators would like to extend that understanding to modular forms of higher rank. Each of the collaborators brings different expertise to the project and thus they will be able to tackle a number of different approaches and topics. They will also attempt to disseminate and advance the study of modular forms through contacts between researchers in the area from North and South America and by bringing three graduate students from historically underrepresented groups from the United States to interact with their peers in Uruguay, while involved in computational and theoretical research projects related to modular forms of rank greater than one.