Ubiquity of Kloosterman sums in Number Theory and Beyond

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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.