Elliptic special functions

虽然椭圆函数和特殊函数都是经典的数学领域，但椭圆特殊函数这一领域是近二十年才建立起来的。它结合了分析、模形式和统计力学的思想，解决了数论(椭圆曲线)、代数(椭圆量子群)、数学物理(塞贝格对偶)等领域的问题。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猜想的解决，以及关于A型根系的椭圆双正交函数的Askey-Wilson-Koorwinder理论的构造。

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.