Riemann zeta function

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Riemann zeta function

[′rē‚män ′zād·ə ‚fəŋk·shən]
(mathematics)
The complex function ζ(z) defined by an infinite series with n th term e -z log n . Also known as zeta function.
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References in periodicals archive ?
Limit Theorems for the Riemann Zeta-Function. Kluwer, Dordrecht, 1996.
On Approximation of Analytic Functions by Periodic Hurwitz Zeta-Functions
Mitrovic, The signs of some constants associated with the Riemann zeta-function, Michigan Math.
The signs of the Stieltjes constants associated with the Dedekind zeta function
Ivic, Riemann zeta-function: theory and applications, Oversea Publishing House, 2003.
On the mean value of [[tau].sup.(e).sub.3](n) over cube-full numbers
where [zeta](s) = [[SIGMA].sup.[infinity].sub.k=1][k.sup.-s] (s > 1) is the Riemann zeta-function. Concerning the computational aspects we shall derive an approximation to [gamma](a) in terms of the function [zeta](s, a), assumed to be numerically known.
An interplay between a generalized-Euler-constant function and the Hurwitz zeta function
[6] Ivic, A., 1985, The Riemann Zeta-Function, Dover, New York, NY.
Generalized twin prime formulas
Clearly, [zeta](s, 1) = [zeta](s) and [zeta](s, 2) = ([2.sup.s] - 1) [zeta](s), where [zeta](s) is the Riemann zeta-function. Therefore, in those cases, [zeta](s, [alpha]) is also universal, however, the approximated function f (s) must be non-vanishing on K.
On Zeros of Some Combinations of Dirichlet L-Functions and Hurwitz Zeta-Functions
The Riemann zeta-function is a special case of the Hurwitz zeta-function:
On the product of Hurwitz zeta-functions
Ivic, The Riemann Zeta-function, John Wiley Sons, 1985.
A short interval result for the Smarandache ceil function and the Dirichlet divisor function
The statistical behaviour and universality properties of the Riemann zeta-function and other allied Dirichlet series.
A Weighted Discrete Universality Theorem for Periodic Zeta-Functions. II
Akatsuka, The Euler product for the Riemann zeta-function in the critical strip.
Euler products beyond the boundary for Selberg zeta functions
In [16], Voronin discovered the universality property of the Riemann zeta-function [zeta](s), s = [sigma] + it, on the approximation of analytic functions from a wide class by shifts [zeta](s + i[tau]), [tau] [member of] R.
Universality Theorems for Some Composite Functions
Where [chi] denotes a Dirichlet character modulo d, L(n, [chi]) denotes the Dirichlet L-function corresponding to[chi], [empty set](d) and [zeta](s) are the Euler function and Riemann zeta-function, respectively.
On partial sums of generalized dedekind sums

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