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Zeta Function

A zeta function is 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,

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

zeta(n)=sum_(k=1)^infty1/(k^n).

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, Weil Conjectures

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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 Resource. https://mathworld.wolfram.com/ZetaFunction.html

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