Luisa Pauline Boneberger: Background on Drinfeld modules

The first talk aims to give the audience some necessary background for the rest of the
seminar. First, set up the notation as explained above and define Drinfeld modules over
C∞. Discuss the exponential function corresponding to a Drinfeld module as well as its
periods [Gos96, §3, 4], [Gek88, §2]. To illustrate the content further, explain the details for
the Carlitz module and define its fundamental period [EGP14, §2,4]. The correspondence
between rank r A-lattices and Drinfeld modules of rank r (Drinfeld Uniformization Theorem)
must be stated, and if time permits, a sketch of its proof would be given [BP20, §2.4]. The
talk should be finalized with a discussion on Anderson generating functions. Its particular
properties, due to Pellarin [Pel08, §4.2], should be explained and a sketch of their proof will
be given [EGP14, Prop. 3.2, Prop. 6.2].