International Seminar on Automorphic Forms

Aaron Pollack (University of California San Diego)

Holomorphic modular forms on Hermitian tube domains have a good notion of Fourier expansion and Fourier coefficients. These Fourier coefficients give the holomorphic modular forms an arithmetic structure: there is a basis of the space of holomorphic modular forms for which all Fourier coefficients of all elements of the basis are algebraic numbers. The group G_2 does not have an associated Shimura variety, but nevertheless there is a class of automorphic functions on G_2 which possess a semi-classical Fourier expansion, called the quaternionic modular forms. I will explain the proof that (in even weight at least 6) the cuspidal quaternionic modular forms possess an arithmetic structure, defined in terms of Fourier coefficients.

https://tu-darmstadt.zoom.us/j/68048280736

The password is the first Fourier coefficient of the modular j-function (as digits).