Dedekind zeta function

The Dedekind zeta function is a mathematical tool that extends the ideas of the famous Riemann zeta function to more complex number systems called number fields. It encodes deep properties about how these numbers, which include roots of polynomials with rational coefficients, are distributed. Specifically, it helps number theorists understand the patterns and distribution of algebraic integers within these fields. Like the Riemann zeta function, it plays a crucial role in exploring fundamental questions about primes and the structure of numbers, and it has connections to advanced areas such as algebraic geometry and cryptography.