香蕉视频

Title: A residue map and a Poisson kernel for Drinfeld cusp forms of rank 3

Abstract:Drinfeld modules and Drinfeld modular forms are certain function field analogs of elliptic curves and classical modular forms. In the first part of this talk, I will introduce these objects, as well as explain analogies and highlight differences compared to the classical case. A new phenomenon appearing is that Drinfeld modules can have arbitrary rank, with Drinfeld modules of rank 2 being the direct analog of elliptic curves.
In analogy with the classical situation, it is very useful to have a combinatorial description of Drinfeld modular forms akin to modular symbols. In the second part of the talk, I will discuss recent work towards such a description in the next case beyond the well understood rank-2 theory. More precisely, I will explain the construction of a residue map between Drinfeld cusp forms of rank 3 and of arbitrary weight, and certain harmonic cocycles on the Bruhat-Tits building. Assuming a non-criticality statement for certain automorphic forms, I will show that this residue map is in fact a Hecke-equivariant isomorphism in favorable situations.

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