Elliptic special functions

椭圆特殊函数

• 批准号: DP140101186
• 负责人: Prof S. Ole Warnaar
• 金额: $ 23.76万
• 依托单位: The University of Queensland
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-01-01 至 2017-04-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140101186
• 关键词: Elliptic; special; functions

Although elliptic functions and special functions are both classical areas of mathematics, the field of elliptic special functions was only established in the last two decades. It combines ideas from analysis, modular forms and statistical mechanics to tackle problems in number theory (elliptic curves), algebra (elliptic quantum groups), mathematical physics (Seiberg duality) and more. This project aims to settle two important problems in the field of elliptic special functions: the resolution of Boyd's conjectures concerning Mahler measures and L-values of elliptic curves, and the construction of an Askey-Wilson-Koorwinder theory of elliptic biorthogonal functions for the A-type root system.

虽然椭圆函数和特殊函数都是数学的经典领域，但椭圆特殊函数领域只是在最近二十年才建立起来。它结合了分析，模块化形式和统计力学的思想，以解决数论（椭圆曲线），代数（椭圆量子群），数学物理（Seiberg对偶）等问题。本项目旨在解决椭圆特殊函数领域中的两个重要问题：关于椭圆曲线的Mahler测度和L值的Boyd公式的求解，以及A型根系的椭圆双正交函数的Askey-Wilson-Koorwinder理论的构造。