  We study a subtle inequity in the distribution of unnormalized differences
between imaginary parts of zeros of the Riemann zeta function. We establish a
precise measure which explains the phenomenon, that the location of each
Riemann zero is encoded in the distribution of large Riemann zeros. We also
extend these results to zeros of more general L-functions. In particular, we
show how the rank of an elliptic curve over Q is encoded in the sequences of
zeros of other L-functions, not only the one associated to the curve.
