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
are the corresponding values of the Riemann zeta function
. In practice, Eq.
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
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.