Automorphic L-Functions, Fourier Coefficients, and Applications

自守 L 函数、傅立叶系数和应用

• 批准号: 1201362
• 负责人: Stephen Miller
• 金额: $ 31.45万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-06-01 至 2015-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1201362&HistoricalAwards=false
• 关键词: Automorphic; Functions; Fourier; Coefficients; Applications

The project involves investigations in the analytic theory of automorphic forms. The PI will work with Wilfried Schmid on creating L-functions from automorphic boundary value distributions, and seeks to generalize their archimedean methods to p-adic fields. The PI will also work with the string theorists Michael Green and Pierre Vanhove on automorphic realizations of small real group representations and their Fourier coefficients. Their goal is to produce examples on exceptional groups which shed light on graviton scattering amplitudes. Finally, the PI will work with the cryptographer Ramarathnam Venkatesan on lattice approaches to cryptographic problems.Automorphic forms are a central topic in modern number theory, and their L-functions relate them to an even wider range of current investigations. The work with Green and Vanhove has used automorphic forms to solve questions commonly studied in the string theory literature. The project with Venkatesan studies the security of commonly used commercial cryptographic algorithms.

该项目涉及自动形式的分析理论的研究。 PI将与Wilfried Schmid合作创建自动形态边界值分布的L功能，并试图将其Archimedean方法推广到P-ADIC字段。 PI还将与弦理论家迈克尔·格林（Michael Green）和皮埃尔·范霍夫（Pierre Vanhove）合作，以实现小型真实团体表示及其傅立叶系数的自动实现。 他们的目标是在特殊组上产生例子，以揭示重力散射幅度。 最后，PI将与密码学家Ramarathnam Venkatesan一起在晶格方法中解决密码问题。塑形形式是现代数字理论中的一个核心主题，它们的L函数将它们与当前更广泛的调查有关。 使用绿色和凡霍夫（Vanhove）的工作使用了自动形式来解决弦理论文献中常见研究的问题。 Venkatesan的项目研究了常用的商业加密算法的安全性。