I wrote a new paper. Should I reapply for a postdoc at mathjobs?
As I understand it, "reapply" is merely a technical term in mathjobs and this should cause no problems.  See, for example, the statement "Update (re-apply) applications as many times as you like, or whenever you have new info to add" in MathJobs Workflow &amp; Features.  I don't know why mathjobs uses the term "reapply," which certainly has the potential to cause confusion.  I can't guarantee that nobody will hold it against you, but I'd be very surprised if anyone did (and I think it would be a big mistake on their part).

Updating your application may not be enough if it has already been read.  I'd recommend also e-mailing key people you would like to work with to let them know about your new paper once it is on the arXiv.  Of course you shouldn't spam large numbers of people, but sending out an announcement is perfectly appropriate if you restrict it to people who would genuinely like to hear about the paper for mathematical reasons, and not just as an advertisement for hiring you.