v2 on the ArXiv

December 18, 2009

Our paper on the arXiv is now in v2. Lots of fixes, from the tiny to the medium-small… The exponent is smaller, most importantly. There was also an instance of saying “X” when we meant “not X”, and figuring out what we meant is of course an unreasonable demand on a first-time reader on top of everything else. So there it is. Hopefully it’s beautiful now.

Volberg and Nazarov have found an alternate perspective from which controlling SSV can be done without the analytic continuation stuff, and we will likely take this approach when we attack the more general case. In the general case, we are still stuck with that old, weak estimate — e^{-c\sqrt{\log n}} — and we’d like to do better. We’ll see what the future holds for this problem.

As for myself, I feel a bit burnt out, but I do have some notes on the new approach I’ll try to pick through a little in the coming weeks. But maybe I should be more concerned about getting my spirits up, at least for the near future.