“The arithmetic of Fourier coefficients of automorphic forms on G2”
Martedì 3 Marzo 2025, ore 14:30 - Aula 2AB40 - Aleksander Horawa (Università di Bonn)
Abstract
In 1973, Shimura discovered a way to associate a holomorphic half-integral weight modular form h with a classical cusp form f. Subsequently, in the 1980s, Waldspurger proved a remarkable formula relating squares of the Fourier coefficients of h and quadratic twists of L-values of f. In the spirit of these results, we prove that one can associate “quaternionic” modular forms on the group G2 with dihedral cusp forms f, whose Fourier coefficients are explicitly related to cubic twists of L-values of f. This gives the first examples where a conjecture of Gross from 2000 has been fully verified.
Joint work with Petar Bakić, Siyan Daniel Li-Huerta, and Naomi Sweeting.
