Analytic structures and arithmetic properties of multiple zeta-functions

研究了Weyl群的解析性质、特殊值及其与作用的关系，以及与根系相关的多个ζ函数的泛函关系。我们证明了几个新公式。特别地，我们得到了G_2型根的ζ函数的泛函关系和宇称结果，从C型根的角度得到了Euler-Zagier和的新关系，以及与李群有关的更一般的ζ函数的各种性质。

We studied analytic properties, special values and their relations with actions of Weyl groups, and functional relations for multiple zeta-functions associated with root systems. We proved several new formulas. In particular, we obtained functional relations and parity results for the zeta-function of the root system of type G_2, new relations for Euler-Zagier sums from the viewpoint of root systems of type C, and various properties of more general zeta-functions associated with Lie groups.