A function that can be defined as a Dirichlet series, i.e., is computed as an infinite sum of powers,
![F(n)=sum_(k=1)^infty[f(k)]^n,](/images/equations/ZetaFunction/NumberedEquation1.svg) |
where 
can be interpreted as the set of zeros of some function. The most commonly encountered
zeta function is the Riemann zeta function,
 |
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 SumExplore 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 FunctionCite this as:
Weisstein, Eric W. "Zeta Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ZetaFunction.html