  The existence of a set of d^2 pairwise equiangular complex lines
(equivalently, a SIC-POVM) in d-dimensional Hilbert space is currently known
only for a finite set of dimensions d. We prove that, if there exists a set of
real units in a certain ray class field (depending on d) satisfying certain
congruence conditions and algebraic properties, a SIC-POVM may be constructed
when d is an odd prime congruent to 2 modulo 3. We give an explicit analytic
formula that we expect to yield such a set of units. Our construction uses
values of derivatives of zeta functions at s=0 and is closely connected to the
Stark conjectures over real quadratic fields.
  We verify numerically that our construction yields SIC-POVMs in dimensions 5,
11, 17, and 23, and we give the first exact solution to the SIC-POVM problem in
dimension 23.
