List of zeta functions

Originally, with the zeta function or function in mathematics, the complex function

Meant. Today, these more accurate Riemann zeta function is called, in honor of Bernhard Riemann, who made ​​significant work to investigate this function in the complex in 1850. As a real function, the study of the zeta function on Leonhard Euler in the 1730s and 1740s is due, inter alia, certain of the values ​​of the zeta function at positive even arguments and the product formula found.

Since then, many were in definition or properties studied similar or generalized functions, which then also the name of the zeta function was given together with the its discoverer.

The most important other zeta functions are:

  • Airy zeta function
  • Artin Mazursche zeta function
  • Dedekind zeta function
  • Epsteinsche zeta function
  • Hurwitz zeta function
  • Jacobian zeta function
  • Lefschetzsche zeta function
  • Lerchsche zeta function
  • Ninitsche zeta function
  • Selberg zeta function
  • Weierstrass zeta function
  • Primzetafunktion

Also related to the Riemann zeta function, without bearing the " Zeta " in its name, the Dirichlet L- series, Dirichlet eta function η and β are the Dirichlet beta function.

Artin–Mazur zeta function Prime zeta function
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