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zeta function

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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

  • 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

  • Zeta function regularization — In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to superficially divergent sums. The technique is now commonly applied to problems in physics, but… …   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

  • Hurwitz zeta function — In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions. It is formally defined for complex arguments s with Re( s )>1 and q with Re( q )>0 by:zeta(s,q) = sum {n=0}^infty frac{1}{(q+n)^{sThis series …   Wikipedia

  • Complex network zeta function — Different definitions have been given for the dimension of a complex network or graph. For example, metric dimension is defined in terms of the resolving set for a graph. Dimension has also been defined based on the box covering method applied to …   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

  • Lerch zeta function — In mathematics, the Lerch zeta function, sometimes called the Hurwitz Lerch zeta function, is a special function that generalizes the Hurwitz zeta function and the polylogarithm. It is named after Mathias Lerch [http://www groups.dcs.st… …   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

  • Multiple zeta function — For a different but related multiple zeta function, see Barnes zeta function. In mathematics, the multiple zeta functions generalisations of the Riemann zeta function, defined by and converge when Re(s1)+...+Re(si) > i for all i.… …   Wikipedia

  • Artin-Mazur zeta function — In mathematics, the Artin Mazur zeta function is a tool for studying the iterated functions that occur in dynamical systems and fractals.It is defined as the formal power series :zeta f(z)=exp sum {n=1}^infty extrm{card} left( extrm{Fix} (f^n)… …   Wikipedia

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