Noun
zeta function (plural zeta functions)
(mathematics) function of the complex variable s that analytically continues the sum of the infinite series
∑
n
=
1
∞
1
n
s
{\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{s}}}}
that converges when the real part of s is greater than 1.
Hypernym: 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
Globally convergent series A globally convergent series for the zeta function, valid for all complex numbers s except for some integer n, was conjectured by Konrad Knopp and proven by Helmut Hasse in 1930 (cf. Source: Internet
He proved the functional equation for the zeta function (already known to Euler), behind which a theta function lies. 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
Open questions Zeta function and the Riemann hypothesis main Plot of the zeta function ζ(s). 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