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 ?
In case K = Q, the Laurent expansion of the Riemann zeta function [zeta](s) at its pole s = 1 is given by
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
(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;
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
And those of the form 1/[[alpha].sup.k.sub.n] can be evaluated using the Riemann Zeta function [20].
for a > 0, where [zeta](j, a) = [[SIGMA].sup.[infinity].sub.i=0][(a + i).sup.-j] is the generalized Riemann zeta function known also as Hurwitz zeta function.
Bradley, Searching symbolically for Apery-like formulae for values of the Riemann zeta function, SIGSAM Bulletin of Algebraic and Symbolic Manipulation, Association of Computing Machinery, 30 (1996), no.
Among the poles of the meromorphic function Z(s) are the roots p of the Riemann zeta function in the critical strip 0 < [sigma]< 1, which is clear from Eq.