# 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.
References in periodicals archive ?
It is known that the multiple sine function has interesting applications: the Kronecker limit formula for real quadratic fields ([13]), expressions of special values of the Riemann zeta and Dirichlet L-functions ([9]), the calculation of the gamma factors of Selberg zeta functions ([9]), expression of solutions to the quantum Knizhnik-Zamolodchikov equation ([7]) and so on.
Mason and Snaith apply the method that Conrey and Snaith used to calculate the n-correlation of the zeros of the Riemann zeta function to the zeros of families of L-functions with orthogonal or symplectic symmetry.
The estimation of the parameter C is done through the inverse of the Riemann zeta function as follows:
Some probabilistic value distributions of the Riemann zeta function
Please note the following corrections to the article Riemann zeta zeros from an asymptotic perspective published in ASMJ Volume 29 Number 2, 2015:
(i) to generalise efficient congruencing to approximately translation invariant systems, and explore consequent applications to Diophantine problems such as Waring~s problem, restriction problems from discrete Fourier analysis, and bounds for the Riemann zeta function within the critical strip;
Riemann's solution is related to a function called the 'Riemann Zeta' function and the related distribution of points on the integer number line for which the function becomes 0.
Among the topics are modular functions and Eisenstein series, the Riemann zeta function, Euler's formulas and functional equations, functional equations, a linear space of solutions, and the multidimensional Poisson summation formula.
The Hurwitz-Lerch zeta function contains, as its special cases, the Riemann zeta function f(s), the Hurwitz zeta function f(s, a), and the Lerch zeta function [l.sub.s]([xi]) defined by
In mathematics, the Bernoulli polynomials occur in the study of many special functions and in particular the Riemann zeta function and the Hurwitz zeta function.
And those of the form 1/[[alpha].sup.k.sub.n] can be evaluated using the Riemann Zeta function [20].

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