Modular forms on G_2
Aaron Pollack - UCSD
Following work of Gross-Wallach, Gan-Gross-Savin defined what are called "modular forms" on the split exceptional group G_2. These are a special class of automorphic forms on G_2. I'll review their definition, and give an update about what is known about them. Results include a construction of cuspidal modular forms with all algebraic Fourier coefficients, and the exact functional equation of the completed standard L-function of certain cusp forms. The results on L-functions are joint with Fatma Cicek, Giuliana Davidoff, Sarah Dijols, Trajan Hammonds, and Manami Roy.
Password: The order of the permutation group on 9 elements.