Elliptic cocycle for GLN(ℤ) and Hecke operators
Time: Thu, 2 Jul 2020, 16:00-17:00
Place: Online
Speaker: Hao Zhang (Sorbonne Université)
Abstract:
A classical result of Eichler, Shimura and Manin asserts that the map that assigns to a cusp form f its period polynomial rf is a Hecke equivariant map. We propose a generalization of this result to a setting where rf is replaced by a family of rational function of N variables equipped with the action of GLN(ℤ). For this purpose, we develop a theory of Hecke operators for the elliptic cocycle recently introduced by Charollois. In particular, when f is an eigenform, the corresponding rational function is also an eigenvector respect to Hecke operator for GLN. Finally, we give some examples for Eisenstein series and the Ramanujan Delta function.
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