The Riemann zeta function is defined as the analytic continuation of the function defined for σ > 1 by the sum of the preceding series.

Zeta functions are typically analogues or generalizations of the Riemann zeta function. Examples include Dedekind zeta functions of number fields, and zeta functions of varieties over finite fields. They are typically initially defined as formal generating functions, but often admit analytic continuations.

The Riemann zeta function is defined as the analytic continuation of the function defined for σ > 1 by the sum of the preceding series.