Here is a quick update to the last post about (restricted) mod-Cauchy convergence; I’ve investigated numerically the behavior of the renormalized averages

(see the post for the notation) for some values of *t*, to see if the limitation to

in Vardi’s result could be a mere artifact of the method. Here are some graphs representing these empirical averages for

(click to see the full pictures):

In particular, note that in the last picture, the vertical scale runs from -300 to 300, more or less, compared with oscillations between 0.5 and 1.5 in the third. So it seems pretty convincing evidence that the limit as *N* goes to infinity does not exist when *t* is large.

(__Note__: the empirical average for *N=5000* involves about 8,000,000 Dedekind sums).