论文标题
扭转的绝对Zeta函数的绝对Euler产品表示，免费Noetherian $ \ mathbb {f} _1 $ -scheme
The absolute Euler product representation of the absolute zeta function for a torsion free Noetherian $\mathbb{F}_1$-scheme
论文作者
论文摘要
满足特定条件的$ \ mathbb {z} $的方案$ x $的绝对Zeta函数，将满足某个条件的限制定义为$ p \至1 $的$ p \至1 $的Zeta Zeta函数的$ x \ otimes \ otimies \ Mathbb {f} _p $。在2016年，在计算出一些特定方案的绝对Zeta函数之后，黑川建议，超过$ \ Mathbb {Z} $的一般方案的绝对Zeta函数应该具有无限的产品结构，他称其称为绝对Euler产品。在本文中，使用Free Noetherian $ \ Mathbb {f} _1 $ -Scheme制定了他的建议，由Connes和Consani定义，我们给出了他的建议。此外，我们表明绝对Euler产品的每个因素均来自$ \ Mathbb {f} _1 $ -Scheme的计数函数。
The absolute zeta function for a scheme $X$ of finite type over $\mathbb{Z}$ satisfying a certain condition is defined as the limit as $p\to 1$ of the congruent zeta function for $X\otimes\mathbb{F}_p$. In 2016, after calculating absolute zeta functions for a few specific schemes, Kurokawa suggested that an absolute zeta function for a general scheme of finite type over $\mathbb{Z}$ should have an infinite product structure which he called the absolute Euler product. In this article, formulating his suggestion using a torsion free Noetherian $\mathbb{F}_1$-scheme defined by Connes and Consani, we give a proof of his suggestion. Moreover, we show that each factor of the absolute Euler product is derived from the counting function of the $\mathbb{F}_1$-scheme.
