Mock Theta Functions
March 3rd, 2007 by WaltMock theta function are a mysterious family of functions defined by Srinivasa Ramanujan. Ramanujan defined them in a letter to G. H. Hardy. Only part of his letter survives, so the actual definition of what makes a function a mock theta function has been lost. The surviving remnant contains examples which make the resemblace to theta functions clear.
I ran across this press release put out by the University of Wisconsin-Madison about a breakthrough in mock theta functions, and I had no idea what they were actually announcing. The best I can piece together is that Sander Zwegers, in his dissertation gave the first general definition of mock theta functions that included most of Ramanujan’s examples, and that this work was extended by Kathrin Bringmann and Ken Ono. Some details can be found in this preprint.
March 5th, 2007 at 4:42 pm
I’ve discussed this with two different houseguests, and at a monthly party where JPL/NASA people mingle with film-making industry people. Those folks who don’t know or care about Math still found this a fascinating human interest story. It goes beyond Ramanujan (for those who didn’t know him, I told The Taxicab Number anecdote) to the unusual nature of not so much solving a long-standing problem, but figuring out from the solutions what the problem really is.
March 7th, 2007 at 6:08 pm
Damn! I’m not going to the right parties.
March 8th, 2007 at 6:25 am
Don Zagier gave a series of talks on mock theta functions almost two years ago. I didn’t attend all, but the one I followed carefully gave a complete interpretation of it as holomorphic part of automorphic form for some congruence subgroups. I don’t know how much of this is similar to the work described here.
March 9th, 2007 at 6:53 pm
Zwegers was Zagier’s PhD student, so it’s definitely related.