论文标题
$ \ mathbb {z} $和$ \ mathbb {z}/n \ mathbb {z} $的Zeta函数的球形和特殊值
Volumes of spheres and special values of zeta functions of $\mathbb{Z}$ and $\mathbb{Z}/n\mathbb{Z}$
论文作者
论文摘要
在每个维度中，单位球的体积都被赋予了新的解释，作为$ \ mathbb {z} $的Zeta函数的特殊值的产物，类似于Minkowski和Siegel的音量公式，而算术组理论。为此ZETA功能找到了专门针对加泰罗尼亚数字的Zeta功能的产品公式。此外，推导了各种其他Zeta值的某些封闭形式表达式，特别是导致对Euler的Riemann Zeta函数值的替代观点。
The volume of the unit sphere in every dimension is given a new interpretation as a product of special values of the zeta function of $\mathbb{Z}$, akin to volume formulas of Minkowski and Siegel in the theory of arithmetic groups. A product formula is found for this zeta function that specializes to Catalan numbers. Moreover, certain closed-form expressions for various other zeta values are deduced, in particular leading to an alternative perspective on Euler's values of the Riemann zeta function.
