New techniques for exponential sums over low degree polynomials

低次多项式指数和的新技术

• 批准号: DE220100859
• 负责人: Dr Bryce Kerr
• 金额: $ 25.47万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-05-02 至 2025-05-01
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE220100859
• 关键词: New; techniques; exponential; sums; over

This project aims to obtain new quantitative estimates for Weyl sums over low degree polynomials. Such estimates are fundamental to several areas of number theory. By interfacing techniques from diverse areas of mathematics, including algebraic geometry, analytic number theory, the geometry of numbers and harmonic analysis, this project will provide the first progress on estimating Weyl sums over low degree polynomials in over a century. The expected outcomes include a deeper understanding of Weyl sums and enhanced international collaborations. Such progress will place Australia at the forefront of this important branch of number theory.

本项目旨在获得低次多项式上Weyl和的新的定量估计。这样的估计是数论的几个领域的基础。通过结合不同数学领域的技术，包括代数几何、解析数论、数几何和调和分析，这个项目将在一个多世纪以来在估计低次多项式的Weyl和方面取得第一个进展。预期的结果包括对Weyl Summs的更深入了解和加强国际合作。这样的进展将使澳大利亚站在数论这一重要分支的前沿。