What is.. the Dedekind zeta function?

Abstract

Euler's zeta function in which the sum is taken over all natural numbers is well known. There is a corresponding function called Dedekind zeta function for number fields where the sum is taken over all ideals of the ring of integers.

We will introduce the Dedekind zeta function with a detailed definition of all number theoretical objects that occur and illustrate these objects with examples.

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