Modular forms on G_2


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March 17, 2021 3:00 pm - 4:00 pm
via Zoom Video Conferencing

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.