That’s rude and jejune. Is it just a typo? Freudian, maybe?

]]>It seems to me to be important to be clear what exactly is the model for higher rank curves. We can’t simply take a rank 0 or 1 curve, then “add a non-torsion point”, continue to enforce that the parity stays the same, and then get a rank 2 or 3 curve (even if we could, should we think of these as independent processes? and should it be equally easy to add points to a rank 1 curve as a rank 0 curve?).

The approach via L-functions and random matrix theory seems to give reliable conjectures for quadratic twists having rank 2. There the idea is that random matrix theory gives the distribution of central values. There is an additional discretization constraint coming from BSD that forces the L-value to vanish provided it is sufficiently small. Now you can try to do the same thing for quadratic twists of a rank 1 curve. So then you want to look at BSD in the rank 1 case and use a similar discretization argument. Unfortunately, this is hard because you’ve got the regulator now, and it can jump around in size a lot. This makes the comparison between rank 2 and rank 3 quite difficult from this type of approach.

]]>Makes me wonder how much of a blog post is actually read. ]]>