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The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.
Sigma Zeta (ΣΖ) is a North American honor society founded in 1925 to recognize undergraduate excellence in the natural sciences, computer science, and mathematics. The society's purpose is to encourage and foster the attainment of knowledge in the natural and computer sciences and mathematics. [ 1 ]
The uppercase zeta is not used, because it is normally identical to Latin Z. The lower case letter can be used to represent: The Riemann zeta function in mathematics [3] The Hurwitz Zeta Function in mathematics [4] The Weierstrass zeta-function [5] The damping ratio of an oscillating system in engineering and physics [6]
The Riemann zeta function ζ(z) plotted with domain coloring. [1] The pole at = and two zeros on the critical line.. The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (), is a mathematical function of a complex variable defined as () = = = + + + for >, and its analytic continuation elsewhere.
Viola Margaret Tyler Goings (August 29, 1899 – March 9, 1983) [1] was an American educator, and one of the "Five Pearls", the five founding members of the Black sorority Zeta Phi Beta in 1920. Early life and education
The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function.
Hugh Montgomery at Oberwolfach in 2008. In mathematics, Montgomery's pair correlation conjecture is a conjecture made by Hugh Montgomery () that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is
In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function = =. Zeta functions include: Airy zeta function, related to the zeros of the Airy function; Arakawa–Kaneko zeta function; Arithmetic zeta function