The longstanding conjecture that the nonimaginary solutions 
of
 |
(1)
|
where 
is the Riemann zeta function, are the eigenvalues of an "appropriate" Hermitian
operator 
.
Berry and Keating (1999) further conjecture that this operator is
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
and 
are the position and conjugate momentum operators, respectively, and multiplication
is noncommutative. Note that 
is symmetric but might have nontrivial deficiency indices,
so while physicists define this operator to be Hermitian, mathematicians do not.
and the Riemann Zeros." In