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arithmetic zeta function
In mathematics, the arithmetic zeta function is a zeta function associated with a scheme of finite type over integers. The arithmetic zeta function generalizes the Riemann zeta function and Dedekind zeta function to higher dimensions. The arithmetic zeta function is one of the most-fundamental objects of number theory.
==Definition==
The arithmetic zeta function is defined by an Euler product analogous to the Riemann zeta function:
:
where the product is taken over all closed points of the scheme . Equivalently, the product is over all points whose residue field is finite. The cardinality of this field is denoted .
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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