Michael Andrew Henry: A new class of automorphic forms

A new class of automorphic forms Michael Andrew Henry (TU Graz)

Abstract: We introduce functions developed in our thesis that are generalizations of automorphic forms: the so-called Hecke vector-forms. In the introduction of these functions, we relate them to well-known combinatorial structures, such as binomial convolutions and Pascal matrices. Time permitted, we discuss how they generalize a well-known Hankel determinant evaluation due to Garvan and also some applications as generating functions. This talk is not aimed at specialists in automorphic forms, but a general mathematical audience.