Arithmetic zeta function

The arithmetic zeta function, often associated with number theory, is a generalization of the Riemann zeta function, which traditionally sums over integers. The arithmetic zeta function, denoted by \( \zeta(s) \), is defined in various ways depending on the context, typically involving sums or products over prime numbers or algebraic structures. One prominent example of an arithmetic zeta function is the **Dedekind zeta function** associated with a number field.