Tate's thesis seminar

Tate's thesis seminar -- Fall 2009

References (by Kalin)

  1. Gelbart's lecture: It is the best 3-page overview of Tate's thesis I found. In addition to the Hecke and Tate's versions of the theorem, and the example I presented (calculated also in a way that I skipped), it also contains the statement of Tate's local theorem.
  2. Knapp's articles in Notices, on Harmonic Analysis (HERE and HERE): leisurely read, but very intellectually stimulating, a necessity before jumping in fully on the Fourier, theta, and the other calculations bandwagon.
  3. Buzzard's notes/slides from a course on Tate's Thesis (HERE and HERE): I find these notes a nice read, because of their informal style, the writer's personal perspective, and the abundance of insight. (For example, after seeing Tate's local theorem in the first reference, one might think that one could get the MC&FEq for L-functions straightforward from the local versions. This is not the case, as Buzzards explains.)
  4. Keith Conrad also did a course on Tate's thesis, and since it was geared to an undergrad(?) audience, you may find here things that are not worked out at any of the fancy books.
  5. By the end of the week I will return Ramakrishnan-Valenza book (a.k.a "Tate's Thesis for Dummies" as (I think) David Freed called it) in the library, so other people could take a look at it.