Eisenstein classes and generating series of modular symbols in $\mathrm{SL}_N$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909999317385216 |
|---|---|
| author | Branchereau, Romain |
| author_facet | Branchereau, Romain |
| contents | 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 Poincaré 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08690 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eisenstein classes and generating series of modular symbols in $\mathrm{SL}_N$ Branchereau, Romain Number Theory 11F03, 11F11, 11F23, 11F27, 11F30, 11F67, 53C07, 53C22, 53C30, 55N45 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 Poincaré 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. |
| title | Eisenstein classes and generating series of modular symbols in $\mathrm{SL}_N$ |
| topic | Number Theory 11F03, 11F11, 11F23, 11F27, 11F30, 11F67, 53C07, 53C22, 53C30, 55N45 |
| url | https://arxiv.org/abs/2411.08690 |