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arXiv · 2411.08690

Eisenstein classes and generating series of modular symbols in $\mathrm{SL}_N$

Romain Branchereau
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Abstract

We define a theta lift between the homology in degree $N-1$ of a locally symmetric space associated to $\mathrm{SL}_N(\mathbb{R})$ and the space of modular forms of weight $N$, similar to the Kudla-Millson lift in the orthogonal setting. We show that the Fourier coefficients of this lift are Poincar\'e duals of modular symbols associated to maximal parabolic subgroups. The constant term is a canonical cohomology classes obtained by transgressing the Euler class of a torus bundle. When $N=2$, we show that the lift surjects on the space of weight 2 modular forms spanned by an Eisenstein series and the eigenforms with non-vanishing L-function.

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Romain Branchereau. 2024-11-13. Eisenstein classes and generating series of modular symbols in $\mathrm{SL}_N$. https://arxiv.org/abs/2411.08690

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