The Dedekind zeta function is a mathematical function associated with a number field, which is a specific type of algebraic structure in number theory. It generalizes the Riemann zeta function and encodes important information about the field's arithmetic properties, such as the distribution of its prime ideals. Defined as a series over the non-zero ideals of the number field, the Dedekind zeta function plays a crucial role in algebraic number theory. It is used to study various properties, including class numbers and the behavior of L-functions, which are central to modern number theory and related areas like algebraic geometry and modular forms.