A Cohen-Zagier modular form on G_2
Aaron Pollack (UCSD)
Abstract: I will report on joint work with Spencer Leslie where we define an analogue of the Cohen-Zagier Eisenstein series to the exceptional group $G_2$. Recall that the Cohen-Zagier Eisenstein series is a weight $3/2$ modular form whose Fourier coefficients see the class numbers of imaginary quadratic fields. We define a particular modular form of weight $1/2$ on $G_2$, and prove that its Fourier coefficients see (certain torsors for) the 2-torsion in the narrow class groups of totally real cubic fields. In particular: 1) we define a notion of modular forms of half-integral weight on certain exceptional groups, 2) we prove that these modular forms have a nice theory of Fourier coefficients, and 3) we partially compute the Fourier coefficients of a particular nice example on G_2.
number theory
Audience: researchers in the topic
Comments: pre-talk at 1:20pm
Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.
Organizers: | Kiran Kedlaya*, Alina Bucur, Aaron Pollack, Cristian Popescu, Claus Sorensen |
*contact for this listing |