It constrains the function f of z in the plane of an open disk with radius less than 1/4 according to the Voronin Universality Theorem.  
The close distribution of its solutions is known as Lehmer's Phenomenon.  It constrains the function f of z in the plane of an open disk with radius less than 1/4 according to the Voronin Universality Theorem.  The eigenvalues of a suitable Hermitian operator are given by its nonimaginary solutions at one half plus i times E sub-n according to the Berry Conjecture.  For the right half plane, it is given by the Dirichlet eta function, and it may be extended by the reflection functional equation to the entire complex plane, though it contains a singularity for the case s equals 1.  FTP, name this special function defined as the natural analytic extension of the sum over every positive integer n of 1 over n to the s, whose non-trivial zeros may have real part equal to one half.
The close distribution of its solutions is known as Lehmer's Phenomenon.  
Riemann zeta function