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Integral of the prime zeta function
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External links
* [http://mathworld.wolfram.com/PrimeZetaFunction.html Prime Zeta Function, in Wolfram Mathworld]
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Zeta function — A zeta function is a function which is composed of an infinite sum of powers, that is, which may be written as a Dirichlet series::zeta(s) = sum {k=1}^{infty}f(k)^s Examples There are a number of mathematical functions with the name zeta function … Wikipedia
Prime-counting function — In mathematics, the prime counting function is the function counting the number of prime numbers less than or equal to some real number x cite book |first=Eric |last=Bach |coauthors=Shallit, Jeffrey |year=1996 |title=Algorithmic Number Theory… … Wikipedia
Riemann zeta function — ζ(s) in the complex plane. The color of a point s encodes the value of ζ(s): dark colors denote values close to zero and hue encodes the value s argument. The white spot at s = 1 is the pole of the zeta function; the black spots on the… … Wikipedia
Zeta function universality — In mathematics, the universality of zeta functions is the remarkable property of the Riemann zeta function and other, similar, functions, such as the Dirichlet L functions, to approximate arbitrary non vanishing holomorphic functions arbitrarily… … Wikipedia
Dedekind zeta function — In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζK(s), is a generalization of the Riemann zeta function which is obtained by specializing to the case where K is the rational numbers Q. In particular,… … Wikipedia
Selberg zeta function — The Selberg zeta function was introduced by Atle Selberg in the 1950s. It is analogous to the famous Riemann zeta function :zeta(s) = prod {pinmathbb{P frac{1}{1 p^{ s where mathbb{P} is the set of prime numbers. The Selberg zeta function uses… … Wikipedia
Riemann zeta function — ▪ mathematics function useful in number theory for investigating properties of prime numbers (prime). Written as ζ(x), it was originally defined as the infinite series ζ(x) = 1 + 2−x + 3−x + 4−x + ⋯. When x = 1, this series is called the… … Universalium
Local zeta-function — In number theory, a local zeta function is a generating function : Z ( t ) for the number of solutions of a set of equations defined over a finite field F , in extension fields Fk of F . FormulationThe analogy with the Riemann zeta function… … Wikipedia
Ihara zeta function — In mathematics, the Ihara zeta function closely resembles the Selberg zeta function, and is used to relate the spectrum of the adjacency matrix of a graph G = (V, E) to its Euler characteristic. The Ihara zeta function was first defined by… … Wikipedia
Igusa zeta-function — In mathematics, an Igusa zeta function is a type of generating function, counting the number of solutions of an equation, modulo p , p 2, p 3, and so on. Definition For a prime number p let K be a p adic field, i.e. [K: mathbb{Q} p] … Wikipedia
