Fast algorithms for zeta functions of algebraic varieties

代数簇 zeta 函数的快速算法

• 批准号: DP150101689
• 负责人: Dr David Harvey
• 金额: $ 22.13万
• 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 Projects
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-01-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP150101689
• 关键词: Fast; algorithms; zeta; functions; algebraic

The project aims to develop new algorithms for counting the number of solutions to polynomial equations in several variables. This fundamental counting problem appears in many areas of mathematics and computer science, such as number theory and cryptography. The aim of the project is to develop algorithms that are more efficient and that are able to handle much larger problems than existing algorithms. The new algorithms are expected to have applications to the numerical investigation of important unsolved problems in number theory, such as the Sato-Tate, Lang-Trotter and Birch-Swinnerton-Dyer conjectures.

该项目旨在开发新的算法，用于计算多个变量多项式方程的解的数量。这个基本的计数问题出现在数学和计算机科学的许多领域，如数论和密码学。该项目的目的是开发更有效的算法，能够处理比现有算法大得多的问题。新的算法有望应用于数论中未解决的重要问题的数值研究，如佐藤-塔特猜想、朗-特罗特猜想和伯奇-斯温纳顿-戴尔猜想。