Mock Modular Forms Program Seminar: Martin Raum, ETH Zurich

Martin Raum, ETH Zurich

Title: Siegel Product Expansion in M24 Moonshine
Speaker: Martin Raum, ETH Zurich
Date: Thursday, September 19, 2013
Time: 2:00pm – 3:30pm
Place: Seminar Room 313, Simons Center




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Abstract: We briefly revisit product expansions that were considered by Cheng, and Cheng and Duncan in the context of $M_{24}$-moonshine. To each conjugacy class $g$ of $M_{24}$, they attached a convergent product expansion $\Phi_g$ on the Siegel upper half plane of degree 2. It is expected that they are Siegel modular forms of some level which can be predicted in terms of properties of g alone.

We describe how to linearize this problem and then solve it by aid of computers in the case that the predicted level is a prime power. We end the talk by summarizing implications on representations of $\Phi_g$ as additive lifts.