Studies on various multiple zeta-functions associated with root systems

量子规范理论中的配分函数和数学中的zeta函数在每个领域都扮演着基本而重要的角色，但在某些情况下它们恰好重合。其中包括Witten Zeta函数。这些Zeta函数在正整数处的特殊值是主要研究对象，应该从不同的角度进行研究。对于这个问题，我们建立了一种统一的方法，通过它们的母函数来处理这些值。我们还从根系的角度得到了相关的Zeta函数和超几何函数的新的函数关系和公式。

Both partition functions in quantum gauge theories and zeta-functions in mathematics, which play fundamental and important roles in each area, happen to coincide in some cases. Among them are the Witten zeta-functions. Special values of these zeta-functions at positive integers are the main objects and should be studied from various viewpoints. For this problem, we established a unified way to treat these values via their generating functions. We also obtained new functional relations and formulas for related zeta-functions and hypergeometric functions from the viewpoint of root systems.