TITLE: What is Ricardo Pérez-Marco's eñe product? Does it explain his statistical results on differences of zeta zeros?
QUESTION [29 upvotes]: The number theory community here at University of Michigan is abuzz with talk of this paper recently posted to the arxiv.  If you haven't seen it already, the punch line is that the global differences of imaginary parts of zeta zeros show an unusual tendency not to be close to imaginary parts of zeta zeros.  "Riemann zeros repel their deltas."
The people I have talked to have said that this simple observation appears to be completely new and potentially groundbreaking.  Here are my questions:
1) Has anyone independently verified these statistics?  (See my histograms below, and also the excellent graphs in Jonathan Bober's answer.)
2) The author discusses the "eñe product" as a source of a mathematical explanation for his observation, and he refers to his own unpublished manuscripts in which he introduces this product.  Are these manuscripts available?  Does anyone have any reference which defines the eñe product?
Finally, any insights into Marco's results would be much appreciated.
The histograms (produced in Mathematica) are of the deltas of the first 10000 zeros of $\zeta(s)$ falling in $[100, 110]$ and $[190, 200]$, respectively.  The purple bars show the locations of the zeros.

REPLY [12 votes]: My student, Brad Rodgers, has just posted a paper on the arXiv at http://arxiv.org/abs/1203.3275 which proves a partial result towards the repulsion effect (that differences of two imaginary parts of Riemann zeroes tend to avoid another Riemann zero), in the spirit of Montgomery's partial result towards his pair correlation conjecture (i.e. this repulsion effect can be detected when tested against sufficiently band-limited test functions, assuming RH).
Ultimately, the reason for this repulsion lies in the obvious approximate formula
$$ |\Lambda(n)|^2 \approx \Lambda(n) \log n$$
where $\Lambda$ is the von Mangoldt function.  If one compares this with the explicit formula, which is formally of the form
$$ \Lambda(n) = 1 - \sum_\rho n^{\rho-1} + \ldots$$
one begins to see the negative correlation between differences of imaginary parts of zeroes $\rho$ (which show up in the expansion of $|\Lambda|^2$) and in the imaginary parts of zeroes themselves.  (Making this intuition rigorous, though, is somewhat non-trivial, requiring manipulations similar to those in Montgomery's original paper to deal with the fact that the explicit formula as given above is only convergent in a very weak sense.)
EDIT: it is likely that a similar analysis would also explain why Riemann zeroes correlate with differences of zeroes of other functions.  For instance, starting from $|\Lambda(n) \chi(n)|^2 \approx \Lambda(n) \log n$, one can predict that differences of imaginary parts of zeroes of a Dirichlet L-function should repel away from the imaginary part of zeroes of zeta.