Automorphic L-Functions, Fourier Coefficients, and Applications

该项目涉及自同构形式分析理论的研究。PI将与Wilfried Schmid合作，从自同构边值分布中创建l函数，并寻求将它们的阿基米德方法推广到p进域。PI还将与弦理论家Michael Green和Pierre Vanhove一起研究小实数群表示及其傅里叶系数的自同构实现。他们的目标是在特殊群体中产生例子来阐明重子散射振幅。最后，PI将与密码学家Ramarathnam Venkatesan合作，研究密码学问题的格方法。自同构形式是现代数论中的一个中心话题，它们的l函数将它们与当前更广泛的研究联系起来。Green和Vanhove的工作使用自同构形式来解决弦理论文献中通常研究的问题。与Venkatesan合作的项目研究了常用商业加密算法的安全性。

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.