  We show that there are an infinite number of Riemann zeros on the critical
line, enumerated by the positive integers $n=1,2,\dotsc$, whose ordinates can
be obtained as the solution of a new transcendental equation that depends only
on $n$. Under weak assumptions, we show that the number of such zeros already
saturates the counting formula for the numbers of zeros on the entire critical
strip. These results thus constitute a concrete proposal toward verifying the
Riemann hypothesis. We perform numerical analyses of the exact equation, and
its asymptotic limit of large ordinate. The starting point is an explicit
analytical formula for an approximate solution to the exact equation in terms
of the Lambert $W$ function. In this way, we neither have to use Gram points or
deal with violations of Gram's law. Our numerical approach thus constitutes a
novel method to compute the zeros. Employing these numerical solutions, we
verify that solutions of the asymptotic version are accurate enough to confirm
Montgomery's and Odlyzko's pair correlation conjectures and also to reconstruct
the prime number counting function.
