A function that can be defined as a Dirichlet series, i.e., is computed as an infinite sum
of powers,

where
can be interpreted as the set of zeros of some function. The most commonly encountered
zeta function is the Riemann zeta function,

## See also

Airy Zeta Function,

Dedekind Function,

Dirichlet Beta Function,

Dirichlet Eta Function,

Dirichlet
L-Series,

Dirichlet Lambda Function,

Dirichlet Series,

Epstein
Zeta Function,

Jacobi Zeta Function,

Nint Zeta Function,

Periodic
Zeta Function,

Prime Zeta Function,

Riemann Zeta Function,

Selberg
Zeta Function,

Zeta-Regularized Product,

Zeta-Regularized Sum
## Explore with Wolfram|Alpha

## References

Ireland, K. and Rosen, M. "The Zeta Function." Ch. 11 in *A
Classical Introduction to Modern Number Theory, 2nd ed.* New York: Springer-Verlag,
pp. 151-171, 1990.## Referenced on Wolfram|Alpha

Zeta Function
## Cite this as:

Weisstein, Eric W. "Zeta Function." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ZetaFunction.html

## Subject classifications