Coefficients of Drinfeld modular forms

Drinfeld modular forms are analogues of classical modular forms over a
function field of positive characteristic. They are defined on a
Drinfeld upper-half plane and have series expansions at infinity. In
this talk, I will explore the action of Hecke operators on such an
expansion, more specifically on the first coefficient. For classical
modular forms, this action is well-understood and gives a perfect
pairing between cusp forms and Hecke algebra. For Drinfeld modular
forms, the pairing may not be perfect in general, as we will see. We
will discuss other consequences.