Theresa Häberle: Background on Drinfeld modular forms

Our goal in the second talk is to give an exposition of known results in the theory of
Drinfeld modular forms, mainly, for the full modular group GL2(A) [Gek88], [Gos80a]. To be
more precise, as a starting point, some background on rigid analytic (holomorphic) functions
on the Drinfeld upper half plane Ω should be given [Rev92, §1–2] (see also [Gos92, §2–5],
[Ste97] and [FvdP04, §2.2]). Later on, weak Drinfeld modular forms as well as Drinfeld
modular forms (for GL2(A)) and their Fourier expansions shall be discussed and the condition
of holomorphy at infinity must be explained [Gek88, §5]. Our main objects for this talk are
going to be illustrated via providing several examples such as Eisenstein series, coefficient
forms, h-function of Gekeler, or more generally, Poincar ́e series [Gek88, (5.9), (5.10), (5.11)].
The results on the C∞-algebra structure of Drinfeld modular forms must be stated [Gek88,
5.12, 5.13]. If time permits, Hecke operators shall be briefly introduced and the notion of
Hecke eigenvalues and Hecke eigenforms will be explained [Gek88, §7].