Zeta Function

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


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,


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


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.

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