Proper noun
(number theory, analytic number theory, uncountable) The function ζ defined by the Dirichlet series
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{\displaystyle \textstyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}={\frac {1}{1^{s}}}+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+{\frac {1}{4^{s}}}+\cdots }
, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said function, being a holomorphic function defined on the complex numbers with pole at 1.
(countable) A usage of (a specified value of) the Riemann zeta function, such as in an equation.
Riemann zeta-function
Alternative spelling of Riemann zeta function
Riemann zeta-function
A restatement of the Riemann hypothesis The connection between the Bernoulli numbers and the Riemann zeta function is strong enough to provide an alternate formulation of the Riemann hypothesis (RH) which uses only the Bernoulli number. Source: Internet
If the polylogarithm function and the Riemann zeta function are not available for calculation, there are a number of ways to do this integration; a simple one is given in the appendix of the Planck's law article. Source: Internet
Riemann introduced new ideas into the subject, the chief of them being that the distribution of prime numbers is intimately connected with the zeros of the analytically extended Riemann zeta function of a complex variable. Source: Internet
The Bernoulli numbers as given by the Riemann zeta function. Source: Internet
The fact that for all complex s ≠ 1 implies that the zeros of the Riemann zeta function are symmetric about the real axis. Source: Internet
The Riemann zeta function represented in a rectangular region of the complex plane. It is generated as a Matplotlib plot using a version of the Domain coloring method. Source: Internet