Ubiquity of Kloosterman sums in Number Theory and Beyond

本项目旨在寻求新的研究Kloosterman和的方法， 结合代数几何方法和分析方法， 强大的统一方法。其重要性在于， 一些位于数论核心的基本问题，如 Dirichlet因子问题和L-函数矩的渐近公式。 该项目的预期成果是， Kloosterman求和的有趣性质，从而为 解析数论中的应用这将提供 通过加深我们对伪随机序列的理解，为诸如密码学等其他领域带来了实质性的好处。

This project aims to seek new methods of investigating Kloosterman sums by combining an algebraic geometry approach with an analytic approach to develop one powerful, unified method. Its significance lies in expected pivotal advances towards several fundamental problems which lie at the heart of number theory such as the Dirichlet Divisor Problem and asymptotic formulas for moments of L-functions. The expected outcome of the project is to provide a deeper understanding of the intriguing nature of Kloosterman sums and thus open new perspectives for applications in analytic number theory. This will provide substantial benefits for other areas such as cryptography by deepening our understanding of pseudorandom sequences.