page_title: Zeta function universality
hierarchical_section_title: Zeta function universality
caption_attribution_description: Illustration of Voronin's universality theorem about the zeta-function in complex analysis
context_page_description: In mathematics, the universality of zeta-functions is the remarkable ability of the Riemann zeta-function and other similar functions to approximate arbitrary non-vanishing holomorphic functions arbitrarily well.
  The universality of the Riemann zeta function was first proven by Sergei Mikhailovitch Voronin in 1975 and is sometimes known as Voronin's Universality Theorem.
context_section_description: In mathematics, the universality of zeta-functions is the remarkable ability of the Riemann zeta-function and other similar functions (such as the Dirichlet L-functions) to approximate arbitrary non-vanishing holomorphic functions arbitrarily well.
  The universality of the Riemann zeta function was first proven by Sergei Mikhailovitch Voronin in 1975 and is sometimes known as Voronin's Universality Theorem.
caption: Any non-vanishing holomorphic function f defined on the strip can be approximated by the ζ-function.
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